{"id":20,"date":"2011-01-27T16:16:04","date_gmt":"2011-01-27T16:16:04","guid":{"rendered":"http:\/\/www.kritiknetz.de\/bgess\/"},"modified":"2026-04-22T10:04:28","modified_gmt":"2026-04-22T10:04:28","slug":"research","status":"publish","type":"page","link":"https:\/\/www.bgess.de\/index.php\/research\/","title":{"rendered":"Research"},"content":{"rendered":"<h2>Research interests<\/h2>\n<p>Stochastic partial differential equations (SPDEs), nonlinear partial differential equations, random dynamical systems, interacting particle systems, machine learning, p<span style=\"font-size: revert; color: initial;\">orous media equations, scalar conservation laws, synchronization by noise, regularization by noise, rough paths.<\/span><\/p>\n<h2>Publications<\/h2>\n<h1>Preprints<\/h1>\n<ol>\n<li><strong>The Incompressible Navier&#8211;Stokes&#8211;Fourier System with Thermal Noise<\/strong><br \/>\nwith Max Sauerbrey, Zhengyan Wu<br \/>\navailable on arXiv <a href=\"https:\/\/arxiv.org\/abs\/2603.26307\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Large Spikes in Stochastic Gradient Descent: A Large-Deviations View<\/strong><br \/>\nwith Daniel Heydecker<br \/>\navailable on arXiv <a href=\"https:\/\/arxiv.org\/abs\/2603.10079\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>The Porous Medium Equation: Multiscale Integrability in Large Deviations<\/strong><br \/>\nwith Daniel Heydecker<br \/>\navailable on arXiv <a href=\"https:\/\/arxiv.org\/abs\/2602.09547\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Probabilistically Strong Solutions to Stochastic Euler Equations<\/strong><br \/>\nwith Robert Lasarzik<br \/>\navailable on arXiv <a href=\"https:\/\/arxiv.org\/abs\/2601.22073\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Ergodicity for SPDEs driven by divergence-free transport noise<\/strong><br \/>\nwith Rishabh S. Gvalani, Adrian Martini<br \/>\navailable on arXiv <a href=\"https:\/\/arxiv.org\/abs\/2601.22056\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Matching Large Deviation Bounds of the Zero-Range Process in the whole space<\/strong><br \/>\nwith Benjamin Fehrman, Daniel Heydecker<br \/>\navailable on arXiv\u00a0<a href=\"https:\/\/arxiv.org\/abs\/2507.23452\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>THINNs: Thermodynamically Informed Neural Networks<\/strong><br \/>\nwith Javier Castro<br \/>\navailable on arXiv\u00a0<a href=\"https:\/\/arxiv.org\/abs\/2509.19467\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Random dynamical systems for McKean&#8211;Vlasov SDEs via rough path theory<\/strong><br \/>\nwith Rishabh S. Gvalani, Shanshan Hu<br \/>\navailable on arXiv\u00a0<a href=\"https:\/\/arxiv.org\/abs\/2507.02449\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>A quantitative central limit theorem for the simple symmetric exclusion process<\/strong><br \/>\nwith Vitalii Konarovskyi<br \/>\navailable on arXiv\u00a0<a href=\"https:\/\/arxiv.org\/abs\/2408.01238\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Higher Order Fluctuation Expansions for Nonlinear Stochastic Heat Equations in Singular Limits<\/strong><br \/>\nwith Zhengyan Wu, Rangrang Zhang<br \/>\navailable on arXiv\u00a0<a href=\"https:\/\/arxiv.org\/abs\/2406.17892\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Optimal Regularity in Time and Space for Nonlocal Porous Medium Type <\/strong><strong>Equations<\/strong><br \/>\nwith Jonas Sauer<br \/>\navailable on arXiv <a href=\"https:\/\/arxiv.org\/abs\/2311.06225\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Ergodicity and random dynamical systems for conservative SPDEs<\/strong><br \/>\nwith Benjamin Fehrman, Rishabh S. Gvalani<br \/>\navailable on arXiv: <a href=\"https:\/\/arxiv.org\/abs\/2206.14789\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<\/ol>\n<h1>Publications in peer-reviewed journals<\/h1>\n<ol start=\"13\">\n<li><strong>Landau-Lifschitz-Navier-Stokes Equations: Large Deviations and Relationship to the Energy Equality<\/strong><br \/>\nwith Daniel Heydecker, Zhengyan Wu<br \/>\nto appear in <em>Annals of Applied Probability<\/em>, arXiv: <a href=\"https:\/\/arxiv.org\/pdf\/2311.02223.pdf\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>A Rescaled Zero-Range Process for the Porous Medium Equation: Hydrodynamic Limit, Large Deviations and Gradient Flow<\/strong><br \/>\nwith Daniel Heydecker<br \/>\nto appear in <em>Communications on Pure and Applied Mathematics, <\/em>arXiv: <a href=\"https:\/\/arxiv.org\/abs\/2303.11289\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Low temperature expansion for the Euclidean \u03a6^4_2-measure<\/strong><br \/>\nwith Kihoon Seong, Pavlos Tsatsoulis<br \/>\nto appear in <em>Transactions of the AMS (TAMS)<\/em>, arXiv <a href=\"https:\/\/arxiv.org\/abs\/2404.14539\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Conservative stochastic PDE and fluctuations of the symmetric simple exclusion process<\/strong><br \/>\nwith Nicolas Dirr, Benjamin Fehrman<br \/>\nto appear in <em>Communications in Mathematical Physics<\/em>, available on arXiv: <a href=\"https:\/\/arxiv.org\/abs\/2012.02126\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Existence of martingale solutions to a stochastic kinetic model of chemotaxis<\/strong><br \/>\nwith Sebastian Herr, Anne Niesdroy<br \/>\nto appear in <em>Nonlinear Differential Equations and Applications NoDEA<\/em>, available on arXiv <a href=\"https:\/\/arxiv.org\/abs\/2504.00450\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Convergence rates for momentum stochastic gradient descent with noise of machine learning type<\/strong><br \/>\nwith Sebastian Kassing<br \/>\nto appear in <em>Mathematical Programming (MAPR),<\/em> available on arXiv: <a href=\"https:\/\/arxiv.org\/abs\/2302.03550\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Conservative stochastic PDEs on the whole space<\/strong><br \/>\nwith Benjamin Fehrman<br \/>\nto appear in <em>Stochastics and Partial Differential Equations: Analysis and Computations<\/em>, arXiv\u00a0<a href=\"https:\/\/arxiv.org\/abs\/2410.00254\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Stabilization by transport noise and enhanced dissipation in the Kraichnan model<\/strong><br \/>\nwith Ivan Yaroslavtsev<br \/>\n<em>J. Evol. Equ. (2025)25:42<\/em>, arXiv: <a href=\"https:\/\/arxiv.org\/abs\/2104.03949\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Conservative SPDEs as fluctuating mean field limits of stochastic gradient descent<\/strong><br \/>\nwith Rishabh S. Gvalani, Vitalii Konarovskyi<br \/>\nto appear in <em>Probability Theory and Related Fields (PTRF),<\/em> arXiv: <a href=\"https:\/\/arxiv.org\/abs\/2207.05705\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Stochastic partial differential equations arising in self-organized criticality<\/strong><br \/>\nwith \u013dubom\u00edr Ba\u0148as, Marius Neu\u00df<br \/>\nto appear in <em>The Annals of Applied Probability (AAoP),<\/em> arXiv: <a href=\"https:\/\/arxiv.org\/abs\/2104.13336\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Solutions to the stochastic thin-film equation for initial values with non-full support<\/strong><br \/>\nwith Konstantinos Dareiotis, Manuel V. Gnann, Max Sauerbrey<br \/>\nto appear in <em>Transactions of the American Mathematical Society<\/em>, arXiv: <a href=\"https:\/\/arxiv.org\/abs\/2305.06017\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Stochastic Modified Flows for Riemannian Stochastic Gradient Descent<\/strong><br \/>\nwith Sebastian Kassing, Nimit Rana<br \/>\nto appear in <em>SIAM Journal on Control and Optimization (SICON)<\/em>, arXiv: <a href=\"https:\/\/arxiv.org\/abs\/2402.03467\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Lyapunov exponents and synchronisation by noise for systems of SPDEs<\/strong><br \/>\nwith Pavlos Tsatsoulis<br \/>\nto appear in <em>Ann. Probab., <\/em>arXiv: <a href=\"https:\/\/arxiv.org\/abs\/2207.09820\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Stochastic Modified Flows, Mean-Field Limits and Dynamics of Stochastic Gradient Descent<\/strong><br \/>\nwith Sebastian Kassing, Vitalii Konarovskyi<br \/>\nto appear in <em>J. Mach. Learn. Res. (JMLR)<\/em>, arXiv: <a href=\"https:\/\/arxiv.org\/abs\/2302.07125\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Well-posedness of the Dean-Kawasaki and the nonlinear Dawson-Watanabe<\/strong><br \/>\n<strong>equation with correlated noise<\/strong><br \/>\nwith Benjamin Fehrman<br \/>\nto appear in <em>Arch. Ration. Mech. Anal. (ARMA)<\/em>, arXiv: <a href=\"https:\/\/arxiv.org\/abs\/2108.08858\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Non-equilibrium large deviations and parabolic-hyperbolic PDE with irregular drift<br \/>\n<\/strong>with Benjamin Fehrman,<br \/>\n<em>Invent. Math.<\/em> 234 (2023), no. 2, 573\u2013636, arXiv: <a href=\"https:\/\/arxiv.org\/abs\/1910.11860\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong><a href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0022123623004263?via%3Dihub\">Long-time behavior of stochastic Hamilton-Jacobi equations<\/a><br \/>\n<\/strong>with Paul Gassiat, Pierre-Louis Lions, Panagiotis E. Souganidis<br \/>\n<em>J. Funct. Anal.<\/em> 286 (2024), no. 4, Paper No. 110269, 49 pp<em>, <\/em>arXiv: <a href=\"https:\/\/arxiv.org\/abs\/2211.12099\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>SVI solutions to stochastic nonlinear diffusion equations on general measure spaces<\/strong><br \/>\nwith Michael R\u00f6ckner, Weina Wu<br \/>\nto appear in <em>Journal of Evolution Equations<\/em> (2024), arXiv <a href=\"https:\/\/browse.arxiv.org\/abs\/2402.01479\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Numerical approximation of singular-degenerate parabolic stochastic PDEs<\/strong><br \/>\nwith Lubom\u00edr Ba\u0148as, Christian Vieth<br \/>\nto appear in: <em>IMA Journal of Numerical Analysis<\/em>, arXiv: <a href=\"https:\/\/arxiv.org\/abs\/2012.12150\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Thermodynamically consistent and positivity-preserving discretization of the thin-film equation with thermal noise<br \/>\n<\/strong>with Rishabh Gvalani, Florian Kunick, Felix Otto<br \/>\n<em>Math. Comp.<\/em> 92 (2023), no. 343, 1931\u20131976, arXiv: <a href=\"https:\/\/arxiv.org\/abs\/2109.06083\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Optimal regularity in time and space for stochastic porous medium equations<br \/>\n<\/strong>with Stefano Bruno, Hendrik Weber<br \/>\n<em>Ann. Probab.<\/em> 50 (2022), no. 6, 2288\u20132343,, arXiv: <a href=\"https:\/\/arxiv.org\/abs\/2110.01637\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a><span style=\"color: initial;\">.<\/span><\/li>\n<li><strong>Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations<br \/>\n<\/strong>with Sebastian Becker, Arnulf Jentzen, Peter E. Kloeden<br \/>\n<em>Stoch. Partial Differ. Equ. Anal. Comput.<\/em> 11 (2023), no. 1, 211\u2013268.,\u00a0arXiv: <a href=\"https:\/\/arxiv.org\/abs\/1711.02423\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>An example of intrinsic randomness in deterministic PDEs<br \/>\n<\/strong>Franco Flandoli, Francesco Grotto<br \/>\n<em>Stoch. Dyn.<\/em> 22 (2022), no. 7, Paper No. 2240023, 30 pp, arXiv: \u00a0<a href=\"https:\/\/arxiv.org\/abs\/2012.04398\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise<br \/>\n<\/strong>with Konstantinos Dareiotis, Manuel V. Gnann, G\u00fcnther Gr\u00fcn<br \/>\n<em>Arch. Ration. Mech. Anal. (ARMA) 242 (2021), no. 1, 179\u2013234<\/em>: <a href=\"https:\/\/arxiv.org\/abs\/2012.04356\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Porous media equations with multiplicative space-time white noise<\/strong><br \/>\nwith Konstantinos Dareiotis, M\u00e1t\u00e9 Gerencs\u00e9r<br \/>\n<em>Ann. Inst. Henri Poincar\u00e9 Probab. Stat. 57 (2021), no. 4, 2354\u20132371<\/em>: <a href=\"https:\/\/arxiv.org\/abs\/2002.12924\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Path-by-path well-posedness of nonlinear diffusion equations with multiplicative noise<\/strong><br \/>\nwith Benjamin Fehrman<br \/>\n<em>J. Math. Pures Appl. (9) 148 (2021), 221\u2013266.<\/em>: <a href=\"https:\/\/arxiv.org\/abs\/1807.04230\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Convergence rates for the stochastic gradient descent method for non-convex objective functions<\/strong><br \/>\nwith Benjamin Fehrman, Arnulf Jentzen<br \/>\n<em>J. Mach. Learn. Res. (JMLR) 21 (2020), Paper No. 136, 48 pp.<\/em>: <a href=\"https:\/\/arxiv.org\/abs\/1904.01517\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>The stochastic thin-film equation: existence of nonnegative martingale solutions<\/strong><br \/>\nwith Manuel V. Gnann<br \/>\n<em>Stochastic Process. Appl. (SPA) 130 (2020), no. 12, 7260\u20137302<\/em>: <a href=\"https:\/\/arxiv.org\/abs\/1904.08951\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Synchronisation by noise for the stochastic quantisation equation in dimensions 2 and 3<\/strong><br \/>\nwith Pavlos Tsatsoulis<br \/>\n<em>Stoch. Dyn. (Stochastics and Dynamics) 20 (2020), no. 6, 2040006, 17 pp.<\/em>: <a href=\"https:\/\/arxiv.org\/abs\/1910.07769\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Ergodicity for Stochastic Porous Media Equations<\/strong><br \/>\nwith Konstantinos Dareiotis, Pavlos Tsatsoulis<br \/>\n<em>SIAM J. Math. Anal. (SIMA) 52 (2020), no. 5, 4524\u20134564.<\/em> : <a href=\"https:\/\/arxiv.org\/abs\/1907.04605\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Random attractors for locally monotone stochastic partial differential equations<\/strong><br \/>\nwith Wei Liu, Andre Schenke<br \/>\n<em>J. Differential Equations (JDE) 269 (2020), no. 4, 3414\u20133455<\/em>: <a href=\"https:\/\/arxiv.org\/abs\/1908.03539\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Nonlinear diffusion equations with nonlinear gradient noise<\/strong><br \/>\nwith Konstantinos Dareiotis<br \/>\n<em>Electron. J. Probab. (EJP) 25 (2020), Paper No. 35, 43 pp.<\/em>: <a href=\"https:\/\/arxiv.org\/abs\/1811.08356\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Density bounds for solutions\u00a0 to differential equations driven by Gaussian rough paths<\/strong><br \/>\nwith\u00a0Cheng Ouyang, Samy Tindel<br \/>\n<em>J. Theoret. Probab. (Journal of Theoretical Probability) 33 (2020), no. 2, 611\u2013648<\/em>: <a href=\"https:\/\/arxiv.org\/abs\/1712.02740\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Optimal regularity in time and space for the porous medium equation<\/strong><br \/>\nwith Jonas Sauer, Eitan Tadmor<br \/>\n<em>Anal. PDE (Analysis and PDE) 13 (2020), no. 8, 2441\u20132480<\/em>: <a href=\"https:\/\/arxiv.org\/abs\/1902.08632\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Optimal regularity for the porous medium equation<\/strong><br \/>\n<em>J. Eur. Math. Soc. (JEMS) 23 (2021), no. 2, 425\u2013465:<\/em> <a href=\"https:\/\/arxiv.org\/abs\/1708.04408\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Well-posedness of nonlinear diffusion equations with nonlinear, conservative noise<\/strong><br \/>\nwith Benjamin Fehrman<br \/>\n<em>Arch. Ration. Mech. Anal. 233 (2019), no. 1, 249\u2013322<\/em>:\u00a0 <a href=\"https:\/\/arxiv.org\/abs\/1712.05775\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Path-by-path regularization by noise for scalar conservation laws<\/strong><br \/>\nwith Khalil Chouk<br \/>\n<em>J. Funct. Anal. (JFA) 277 (2019), no. 5, 1469\u20131498<\/em>:\u00a0\u00a0 <a href=\"https:\/\/arxiv.org\/abs\/1708.00823\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations<br \/>\n<\/strong>with Sebastian Becker, Arnulf Jentzen, Peter E. Kloeden<br \/>\n<em>BIT (BIT Numerical Mathematics.) 60 (2020), no. 4, 1057\u20131073.<\/em>:\u00a0 <a href=\"https:\/\/arxiv.org\/abs\/1811.01725\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians<\/strong><br \/>\nwith\u00a0Paul Gassiat, Pierre-Louis Lions, Panagiotis E. Souganidis<br \/>\n<em>Probab. Theory Related Fields 176 (2020), no. 1-2, 421\u2013448.<\/em>: <a href=\"https:\/\/arxiv.org\/abs\/1805.08477\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Stochastic nonlinear Fokker-Planck equations<\/strong><br \/>\nwith Michele Coghi<br \/>\n<em>Nonlinear Anal. (Theory, Methods &amp; Applications) 187 (2019), 259\u2013278<\/em>: <a href=\"https:\/\/arxiv.org\/abs\/1904.07894\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Entropy solutions for stochastic porous media equations<\/strong><br \/>\nwith Konstantinos Dareiotis,\u00a0Mat\u00e9 Gerencs\u00e9r<br \/>\n<em>J. Differential Equations 266 (2019), no. 6, 3732\u20133763<\/em>: <a href=\"https:\/\/arxiv.org\/abs\/1803.06953\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Supremum estimates for degenerate, quasilinear stochastic partial differential equations<\/strong><br \/>\nwith Konstantinos Dareiotis<br \/>\n<em>Ann. Inst. Henri Poincar\u00e9 Probab. Stat. 55 (2019), no. 3, 1765\u20131796.<\/em>: <a href=\"https:\/\/arxiv.org\/abs\/1712.06655\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Stochastic continuity equations with conservative noise<\/strong><br \/>\nwith Scott Smith<br \/>\n<em>J. Math. Pures Appl. (JMPA) (9) 128 (2019), 225\u2013263<\/em>:\u00a0<a href=\"https:\/\/arxiv.org\/abs\/1710.04906\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Regularity of solutions to scalar conservation laws with a force<\/strong><br \/>\nwith Xavier Lamy<br \/>\n<em>Ann. Inst. H. Poincar\u00e9 Anal. Non Lin\u00e9aire<\/em> 36 (2019), no. 2, 505\u2013521: <a href=\"https:\/\/arxiv.org\/abs\/1707.06866\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Well-posedness by noise for scalar conservation laws<br \/>\n<\/strong>with\u00a0Mario Maurelli<br \/>\n<em>Comm. Partial Differential Equations (CPDE) 43 (2018), no. 12, 1702\u20131736<\/em>:<a href=\"https:\/\/arxiv.org\/abs\/1701.05393\" target=\"_blank\" rel=\"noopener noreferrer\"> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Regularization by noise for stochastic Hamilton-Jacobi equations<br \/>\n<\/strong>with Paul Gassiat<strong><br \/>\n<\/strong><em>Probab. Theory Related Fields 173 (2019), no. 3-4, 1063\u20131098.<\/em>:\u00a0\u00a0 <a href=\"https:\/\/arxiv.org\/abs\/1609.07074\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Regularization and well-posedness by noise for ordinary and partial\u00a0differential equations<\/strong><br \/>\nto appear in:\u00a0Stochastic Partial Differential Equations and Related Fields,\u00a0<em>Springer Proceedings in Mathematics &amp; Statistics, <\/em>preprint: <a href=\"http:\/\/www.bgess.de\/wp-content\/uploads\/Gess-Regularization-and-well-posedness-by-noise-for-ODE-and-PDE.pdf\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Well-posedness and regularity for quasilinear degenerate<br \/>\nparabolic-hyperbolic SPDE<br \/>\n<\/strong>with Martina Hofmanova<br \/>\n<em>Ann. Probab.<\/em> 46 (2018), no. 5, 2495\u20132544:\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1611.03600\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Stochastic non-isotropic degenerate parabolic-hyperbolic equations<br \/>\n<\/strong>with Panagiotis E. Souganidis<br \/>\n<em>Stochastic Processes and their Applications (SPA) 127 (2017), no. 9, 2961\u20133004<\/em>: <a href=\"https:\/\/arxiv.org\/abs\/1611.01303\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Ergodicity and local limits for stochastic local and nonlocal p-Laplace<br \/>\nequations<br \/>\n<\/strong>with\u00a0Jonas M. T\u00f6lle<strong><br \/>\n<\/strong><em>SIAM Journal on Mathematical Analysis (SIMA) 48 (2016), no. 6, 4094\u20134125:<\/em>\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1507.04545\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong><strong>Stochastic variational inequalities and regularity for degenerate stochastic partial differential equations<br \/>\n<\/strong><\/strong>with\u00a0Michael R\u00f6ckner<br \/>\n<em>Transactions of the AMS 369 (2017), no. 5, 3017\u20133045.<\/em>: <a href=\"http:\/\/arxiv.org\/abs\/1405.5866\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Semi-discretization for stochastic scalar conservation laws with multiple rough fluxes<\/strong><br \/>\nwith Beno\u00eet Perthame, Panagiotis E. Souganidis<br \/>\n<em>SIAM Journal on Numerical Analysis (SINUM) 54 (2016), no. 4, 2187\u20132209:<\/em>\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1512.06056\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Long-time behavior, invariant measures and regularizing effects for stochastic scalar conservation laws<br \/>\n<\/strong>with\u00a0Panagiotis E. Souganidis<br \/>\n<em>Comm. Pure Appl. Math. 70 (2017), no. 8, 1562\u20131597: <\/em><a href=\"http:\/\/arxiv.org\/abs\/1411.3939\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Synchronization by noise<\/strong><br \/>\nwith\u00a0Franco Flandoli, Michael Scheutzow<br \/>\n<em>Probab. Theory Related Fields 168 (2017), no. 3-4, 511\u2013556.<\/em>:<b>\u00a0<\/b><a href=\"http:\/\/arxiv.org\/abs\/1411.1340\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Weak synchronization for isotropic flows<\/strong><br \/>\nwith Michael Cranston, Michael Scheutzow<br \/>\n<em>Discrete Contin. Dyn. Syst. Ser. B (DCDS-B) 21 (2016), no. 9, 3003\u20133014<\/em>:<strong>\u00a0<\/strong> \u00a0<a href=\"http:\/\/arxiv.org\/abs\/1510.09096\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Synchronization by noise for order-preserving random dynamical systems<br \/>\n<\/strong>with\u00a0Franco Flandoli, Michael Scheutzow<br \/>\n<em>The Annals of Probability 45 (2017), no. 2, 1325\u20131350.<\/em>:<strong>\u00a0<\/strong>\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1503.08737\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Stability of solutions to stochastic partial differential equations<br \/>\n<\/strong>with\u00a0Jonas M. T\u00f6lle<strong><br \/>\n<\/strong><em>J. Differential Equations,<\/em> 260 (2016), no. 6, 4973\u20135025:\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1506.01230\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Singular-degenerate multivalued stochastic fast diffusion equations<\/strong><br \/>\nwith Michael R\u00f6ckner<br \/>\n<em>SIAM Journal on Mathematical Analysis (SIMA) 47 (2015), no. 5, 4058\u20134090: <a href=\"http:\/\/arxiv.org\/abs\/1501.01544\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/>.<\/a><\/em><\/li>\n<li><strong>Stochastic scalar conservation laws driven by rough paths<br \/>\n<\/strong>with\u00a0Peter K. Friz<strong><br \/>\n<\/strong><em>Ann. Inst. H. Poincar\u00e9 Anal. Non Lin\u00e9aire\u00a0(AIHP) 33 (2016), no. 4, 933\u2013963<\/em>:\u00a0\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1403.6785\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/>.<\/a><\/li>\n<li><strong>Scalar conservation laws with multiple rough fluxes<br \/>\n<\/strong> with Panagiotis E. Souganidis<br \/>\n<em>Commun. Math. Sci<\/em>. 13 (2015), no. 6, 1569\u20131597.: \u00a0<a href=\"http:\/\/arxiv.org\/abs\/1406.2978\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/>.<\/a><\/li>\n<li><strong><strong><strong>Finite time extinction for stochastic sign fast diffusion and self-organized criticality<br \/>\n<\/strong><\/strong><\/strong><em>Comm. Math. Phys.<\/em><em>,<\/em>\u00a0335 (2015), no. 1, 309\u2013344:<strong>\u00a0<\/strong>\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1310.6971\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong><strong>Jain-Monrad criterion for rough paths<br \/>\n<\/strong><\/strong>with Peter K. Friz, Archil Gulisashvili, Sebastian Riedel<strong><br \/>\n<\/strong>to appear in:<em>\u00a0The Annals of Probability<\/em>, (2014):<strong>\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1307.3460\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/strong><\/li>\n<li><strong>Multi-valued, singular stochastic evolution inclusions.<br \/>\n<\/strong>with Jonas M. T\u00f6lle<br \/>\n<em>J. Math. Pures Appl. (JMPA)<\/em> (9) 101 (2014), no. 6, 789\u2013827:\u00a0<a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0021782413001281\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>,\u00a0arXiv:\u00a0\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1112.5672\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Random attractors for stochastic porous media equations perturbed by space-time linear multiplicative noise.<br \/>\n<\/strong><em>The Annals of Probability,<\/em>\u00a042 (2014), no. 2, 818\u2013864.:\u00a0\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1108.2413\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Finite speed of propagation for stochastic porous media equation.<br \/>\n<\/strong><em>SIAM J. Math. Anal. (SIMA)<\/em>, 45 (2013), no. 5, 2734\u20132766.:\u00a0\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1210.2415\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Random attractors for singular stochastic partial differential equations.<br \/>\n<\/strong><em>J. Differential Equations (JDE),<\/em> 255 (2013), no. 3, 524\u2013559:\u00a0\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1111.0205\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>Random Attractors for Degenerate Stochastic Partial Differential Equations.<br \/>\n<\/strong><em>J. Dynam. Differential Equations (JDDE)<\/em>, 25(1) (2013), 121-157.\u00a0\u00a0<a href=\"http:\/\/www.springerlink.com\/openurl.asp?genre=article&amp;id=doi:10.1007\/s10884-013-9294-5\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a><\/li>\n<li><strong>Strong Solutions for Stochastic Partial Differential Equations of Gradient Type<\/strong><strong>.<br \/>\n<\/strong> <em>J. Funct. Anal. (JFA)<\/em>,\u00a0263(8)(2012),2355-2383.\u00a0<a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0022123612002662\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a><\/li>\n<li><strong><strong>Random attractors for stochastic porous media equations perturbed by space-time linear multiplicative noise. <\/strong><\/strong>(Concise announcement of the results)<br \/>\n<em>Comptes Rendus Mathematique<\/em>,\u00a0350(5\u20136)(2012), 299\u2013302.<a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S1631073X12000428\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a><\/li>\n<li><strong>Random attractors for a class of stochastic partial di\ufb00erential equations driven by general additive noise.<\/strong><br \/>\nwith Wei Liu, Michael R\u00f6ckner<br \/>\n<em>J. Differential Equations (JDE)<\/em>, 251(4-5)(2011), 1225 &#8211; 1253.\u00a0<a href=\"http:\/\/www.math.uni-bielefeld.de\/sfb701\/files\/preprints\/sfb10079.pdf\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a><\/li>\n<li><strong>The Global Random Attractor for a Class of Stochastic Porous Media Equations <\/strong><br \/>\nwith Wolf-J\u00fcrgen Beyn, Michael R\u00f6ckner, Paul Lescot<br \/>\n<em>Comm. Partial Differential Equations (CPDE)<\/em>, 36 (3) (2011), 446 &#8211; 469. <a href=\"http:\/\/www.math.uni-bielefeld.de\/sfb701\/files\/preprints\/sfb10009.pdf\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-34\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a><\/li>\n<\/ol>\n<h1>Theses<\/h1>\n<ul>\n<li>Stochastic Flows induced by Stochastic Partial Differential Equations, Dissertation, University of Bielefeld, 2011<\/li>\n<li>Convexity of Chebyshev sets, Master thesis, Warwick University, 2009<\/li>\n<\/ul>\n<h1>Conference and workshop proceedings<\/h1>\n<ul>\n<li><strong>Regularization by noise for stochastic Hamilton-Jacobi equations<\/strong><br \/>\nbased on joint work\u00a0with Paul Gassiat<br \/>\nOberwolfach Reports\u00a0<strong>24\u00a0<\/strong>(2016),\u00a01349 &#8211; 1353.<br \/>\nProceedings for the workshop: Rough Paths, Regularity Structures and Related Topics,\u00a0May 1-7th, 2016,<br \/>\nMathematisches\u00a0Forschungsinstitut Oberwolfach<\/li>\n<li><strong>Spatial rough path lifts of stochastic convolutions<\/strong><br \/>\nbased on joint work\u00a0with Peter Friz, Archil Gulisashvili, Sebastian Riedel<br \/>\nOberwolfach Reports\u00a0<strong>41 <\/strong>(2012), 17 &#8211; 21.<br \/>\nProceedings for the workshop: Rough Paths and PDEs,\u00a0August 19-25th, 2012,<br \/>\nMathematisches\u00a0Forschungsinstitut Oberwolfach<\/li>\n<\/ul>\n<h1>Electronic publications<\/h1>\n<ul>\n<li><strong>Spatial rough path lifts of stochastic convolutions<br \/>\n<\/strong>with\u00a0Peter Friz, Archil Gulisashvili, Sebastian Riedel<strong><br \/>\n<\/strong>available on arXiv:\u00a0\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1211.0046\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" title=\"pdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<li><strong>On the Variational Regularity of Cameron-Martin paths<br \/>\n<\/strong>with\u00a0Peter K. Friz, Sebastian Riedel<br \/>\navailable on arXiv:\u00a0\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1305.2943\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" title=\"p\ufffcdf-icon-2\" src=\"http:\/\/www.bgess.de\/wp-content\/uploads\/2011\/01\/pdf-icon-2.png\" alt=\"\" width=\"15\" height=\"15\" \/><\/a>.<\/li>\n<\/ul>\n<h2>Coauthors<\/h2>\n<p>(in chronological\u00a0order)<\/p>\n<ul>\n<li><a title=\"Michael R\u00f6ckner\" href=\"http:\/\/www.math.uni-bielefeld.de\/~roeckner\/\" target=\"_blank\" rel=\"noopener noreferrer\">Michael R\u00f6ckner<\/a> (Universit\u00e4t Bielefeld)<\/li>\n<li><a title=\"Wolf-J\u00fcrgen Beyn\" href=\"http:\/\/www.mathematik.uni-bielefeld.de\/~beyn\/\">Wolf-J\u00fcrgen Beyn<\/a> (Universit\u00e4t Bielefeld)<\/li>\n<li><a title=\"Paul Lescot\" href=\"http:\/\/www.univ-rouen.fr\/LMRS\/Persopage\/Lescot\/\">Paul Lescot<\/a> (Universit\u00e9 de Rouen)<\/li>\n<li><a title=\"Wei Liu\" href=\"http:\/\/www.math.uni-bielefeld.de\/sfb701\/people\/view\/632\" target=\"_blank\" rel=\"noopener noreferrer\">Wei Liu<\/a> (Universit\u00e4t Bielefeld)<\/li>\n<li><a href=\"http:\/\/jonas-toelle.com\/\">Jonas M. T\u00f6lle<\/a> (Technische Universit\u00e4t Berlin)<\/li>\n<li><a href=\"http:\/\/page.math.tu-berlin.de\/~friz\/\">Peter Friz<\/a> (Technische Universit\u00e4t Berlin)<\/li>\n<li><a href=\"http:\/\/www.math.ohiou.edu\/people\/directory\/guli\">Archil Gulisashvili<\/a> (Ohio University)<\/li>\n<li><a href=\"http:\/\/page.math.tu-berlin.de\/~riedel\/\">Sebastian Riedel<\/a>\u00a0(Technische Universit\u00e4t Berlin)<\/li>\n<li><a href=\"http:\/\/math.uchicago.edu\/~souganidis\/\">Panagiotis E. Souganidis<\/a> (University of Chicago)<\/li>\n<li><a href=\"http:\/\/users.dma.unipi.it\/flandoli\/\">Franco Flandoli<\/a> (University of Pisa)<\/li>\n<li><a href=\"http:\/\/page.math.tu-berlin.de\/~scheutzow\/\">Michael Scheutzow<\/a> (Technische Universit\u00e4t Berlin)<\/li>\n<li><a href=\"https:\/\/www.math.uci.edu\/people\/michael-cranston\">Michael Cranston<\/a> (University of California, Irvine)<\/li>\n<li><a href=\"http:\/\/www.ann.jussieu.fr\/~perthame\/\">Beno\u00eet Perthame<\/a> (Universit\u00e9 Pierre et Marie Curie)<\/li>\n<li>Paul Gassiat (Universit\u00e9 Paris Dauphine)<\/li>\n<li>Martina Hofmanova (Universit\u00e4t Bielefeld)<\/li>\n<li>Mario Maurelli (TU Berlin)<\/li>\n<li><a href=\"https:\/\/www.math.univ-toulouse.fr\/~xlamy\/index.html\">Xavier Lamy<\/a> (Universit\u00e9 Toulouse)<\/li>\n<li>Khalil Chouk (TU Berlin)<\/li>\n<li>Scott Smith (MPI MIS Leipzig)<\/li>\n<li>Sebastian Becker<\/li>\n<li>Arnulf Jentzen (ETH Z\u00fcrich)<\/li>\n<li>Peter E. Kloeden (Universit\u00e4t Frankfurt)<\/li>\n<li>Konstantinos Dareiotis (MPI MIS Leipzig)<\/li>\n<li>Benjamin Fehrman (MPI MIS Leipzig)<\/li>\n<li>Cheng Ouyang (University of Illinois at Chicago)<\/li>\n<li>Samy Tindel (Purdue University)<\/li>\n<li>Mat\u00e9 Gerencs\u00e9r (IST Austria)<\/li>\n<li>Pierre-Louis Lions (Coll\u00e8ge de France)<\/li>\n<li>Felix Otto (MPI MIS Leipzig)<\/li>\n<li>Rishabh Gvalani\u00a0(MPI MIS Leipzig)<\/li>\n<li>Florian Kunick (MPI MIS Leipzig)<\/li>\n<li>\u013dubom\u00edr Ba\u0148as (Universit\u00e4t Bielefeld)<\/li>\n<li>Ivan Yaroslavtsev (Universit\u00e4t Hamburg)<\/li>\n<li>Christian Vieth (Universit\u00e4t Bielefeld)<\/li>\n<li>Stefano Bruno (University Bath)<\/li>\n<li>Hendrik Weber (University Bath)<\/li>\n<li>Nicolas Dirr (University Cardiff)<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Research interests Stochastic partial differential equations (SPDEs), nonlinear partial differential equations, random dynamical systems, interacting particle systems, machine learning, porous [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"class_list":["post-20","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.bgess.de\/index.php\/wp-json\/wp\/v2\/pages\/20","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.bgess.de\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.bgess.de\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.bgess.de\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.bgess.de\/index.php\/wp-json\/wp\/v2\/comments?post=20"}],"version-history":[{"count":396,"href":"https:\/\/www.bgess.de\/index.php\/wp-json\/wp\/v2\/pages\/20\/revisions"}],"predecessor-version":[{"id":2071,"href":"https:\/\/www.bgess.de\/index.php\/wp-json\/wp\/v2\/pages\/20\/revisions\/2071"}],"wp:attachment":[{"href":"https:\/\/www.bgess.de\/index.php\/wp-json\/wp\/v2\/media?parent=20"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}