{"id":20,"date":"2011-01-27T16:16:04","date_gmt":"2011-01-27T16:16:04","guid":{"rendered":"http:\/\/www.kritiknetz.de\/bgess\/"},"modified":"2026-04-01T07:11:16","modified_gmt":"2026-04-01T07:11:16","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>Landau-Lifschitz-Navier-Stokes Equations: Large Deviations and Relationship to the Energy Equality<\/strong><br \/>\nwith Daniel Heydecker, Zhengyan Wu<br \/>\navailable on 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>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=\"14\">\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 media equations, scalar conservation laws, synchronization by noise, regularization by noise, rough paths. Publications Preprints The Incompressible Navier&#8211;Stokes&#8211;Fourier System with Thermal Noise with Max Sauerbrey, Zhengyan Wu available on arXiv . Large Spikes in Stochastic [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"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":394,"href":"https:\/\/www.bgess.de\/index.php\/wp-json\/wp\/v2\/pages\/20\/revisions"}],"predecessor-version":[{"id":2063,"href":"https:\/\/www.bgess.de\/index.php\/wp-json\/wp\/v2\/pages\/20\/revisions\/2063"}],"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}]}}