Stochastic partial differential equations

Head:
Benjamin Gess (Email, Homepage)

Phone:
+49 (0) 341 - 9959 - 954

Fax:
+49 (0) 341 - 9959 - 658

Address:
Inselstr. 22
04103 Leipzig

Publications

Journal Articles

Sebastian Becker ; Benjamin Gess ; Arnulf Jentzen and Peter E. Kloeden: Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations
In: Stochastics and partial differential equations : analysis and computations, Vol. not yet known, pp. not yet known
Bibtex DOI: 10.1007/s40072-021-00226-6 ARXIV: https://arxiv.org/abs/1711.02423
Journal Open Access

Stefano Bruno ; Benjamin Gess and Hendrik Weber: Optimal regularity in time and space for stochastic porous medium equations
In: The annals of probability, 50 (2022) 6, p. 2288-2343
Bibtex DOI: 10.1214/22-AOP1583 ARXIV: https://arxiv.org/abs/2110.01637
Repository Open Access

Franco Flandoli ; Benjamin Gess and Francesco Grotto: An example of intrinsic randomness in deterministic PDEs
In: Stochastics and dynamics, Vol. not yet known, pp. not yet known
Bibtex DOI: 10.1142/s0219493722400238 ARXIV: https://arxiv.org/abs/2012.04398
Repository Open Access

Konstantinos Dareiotis ; Máté Gerencscér and Benjamin Gess: Porous media equations with multiplicative space-time white noise
In: Annales de l'Institut Henri Poincaré / B, 57 (2021) 4, p. 2354-2371
Bibtex DOI: 10.1214/20-AIHP1139 ARXIV: https://arxiv.org/abs/2002.12924
Repository Open Access

Konstantinos Dareiotis ; Benjamin Gess ; Manuel V. Gnann and Günther Grün: Non-negative martingale solutions to the stochastic thin-film equation with nonlinear gradient noise
In: Archive for rational mechanics and analysis, 242 (2021) 1, p. 179-234
Bibtex DOI: 10.1007/s00205-021-01682-z ARXIV: https://arxiv.org/abs/2012.04356
Journal Open Access

Benjamin J. Fehrman and Benjamin Gess: Path-by-path well-posedness of nonlinear diffusion equations with multiplicative noise
In: Journal de mathématiques pures et appliquées, 148 (2021), p. 221-266
Bibtex DOI: 10.1016/j.matpur.2021.01.004 ARXIV: https://arxiv.org/abs/1807.04230
Repository Open Access

Benjamin Gess: Optimal regularity for the porous medium equation
In: Journal of the European Mathematical Society, 23 (2021) 2, p. 425-465
Bibtex DOI: 10.4171/JEMS/1014 ARXIV: https://arxiv.org/abs/1708.04408
Repository Open Access

Sebastian Becker ; Benjamin Gess ; Arnulf Jentzen and Peter E. Kloeden: Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations
In: BIT : numerical mathematics, 60 (2020) 4, p. 1057-1073
Bibtex DOI: 10.1007/s10543-020-00807-2 ARXIV: https://arxiv.org/abs/1811.01725
Repository Open Access

Konstantinos Dareiotis and Benjamin Gess: Nonlinear diffusion equations with nonlinear gradient noise
In: Electronic journal of probability, 25 (2020), 35
Bibtex DOI: 10.1214/20-EJP436 ARXIV: https://arxiv.org/abs/1811.08356
Journal Open Access

Konstantinos Dareiotis ; Benjamin Gess and Pavlos Tsatsoulis: Ergodicity for stochastic porous media equations with multiplicative noise
In: SIAM journal on mathematical analysis, 52 (2020) 5, p. 4524-4564
Bibtex DOI: 10.1137/19M1278521 ARXIV: https://arxiv.org/abs/1907.04605
Repository Open Access

Benjamin J. Fehrman ; Benjamin Gess and Arnulf Jentzen: Convergence rates for the stochastic gradient descent method for non-convex objective functions
In: Journal of machine learning research, 21 (2020) 136, p. 1-48
Bibtex ARXIV: https://arxiv.org/abs/1904.01517 LINK: https://jmlr.csail.mit.edu/papers/v21/19-636.html
Journal Open Access

Paul Gassiat ; Benjamin Gess ; Pierre-Louis Lions and Panagiotis E. Souganidis: Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians
In: Probability theory and related fields, 176 (2020) 1/2, p. 421-448
Bibtex DOI: 10.1007/s00440-019-00921-5 ARXIV: https://arxiv.org/abs/1805.08477
Repository Open Access

Benjamin Gess and Manuel V. Gnann: The stochastic thin-film equation : existence of nonnegative martingale solutions
In: Stochastic processes and their applications, 130 (2020) 12, p. 7260-7302
Bibtex DOI: 10.1016/j.spa.2020.07.013 ARXIV: https://arxiv.org/abs/1904.08951 LINK: https://www.researchgate.net/publication/332565323
Repository Open Access

Benjamin Gess ; Wei Liu and Andre Schenke: Random attractors for locally monotone stochastic partial differential equations
In: Journal of differential equations, 269 (2020) 4, p. 3414-3455
Bibtex DOI: 10.1016/j.jde.2020.03.002 ARXIV: https://arxiv.org/abs/1908.03539
Repository Open Access

Benjamin Gess ; Cheng Ouyang and Samy Tindel: Density bounds for solutions to differential equations driven by Gaussian rough paths
In: Journal of theoretical probability, 33 (2020) 2, p. 611-648
Bibtex DOI: 10.1007/s10959-019-00967-0 ARXIV: https://arxiv.org/abs/1712.02740
Repository Open Access

Benjamin Gess ; Jonas Sauer and Eitan Tadmor: Optimal regularity in time and space for the porous medium equation
In: Analysis and PDE, 13 (2020) 8, p. 2441-2480
Bibtex DOI: 10.2140/apde.2020.13.2441 ARXIV: https://arxiv.org/abs/1902.08632
Repository Open Access

Benjamin Gess and Pavlos Tsatsoulis: Synchronization by noise for the stochastic quantization equation in dimensions \(2\) and \(3\)
In: Stochastics and dynamics, 20 (2020) 6, 240006
Bibtex DOI: 10.1142/S0219493720400067 ARXIV: https://arxiv.org/abs/1910.07769
Repository Open Access

Khalil Chouk and Benjamin Gess: Path-by-path regularization by noise for scalar conservation laws
In: Journal of functional analysis, 277 (2019) 5, p. 1469-1498
Bibtex DOI: 10.1016/j.jfa.2019.06.005 ARXIV: https://arxiv.org/abs/1708.00823
Repository Open Access

Michele Coghi and Benjamin Gess: Stochastic nonlinear Fokker-Planck equations
In: Nonlinear analysis / A, 187 (2019), p. 259-278
Bibtex DOI: 10.1016/j.na.2019.05.003 ARXIV: https://arxiv.org/abs/1904.07894
Repository Open Access

Konstantinos Dareiotis ; Máté Gerencscér and Benjamin Gess: Entropy solutions for stochastic porous media equations
In: Journal of differential equations, 266 (2019) 6, p. 3732-3763
Bibtex DOI: 10.1016/j.jde.2018.09.012 ARXIV: https://arxiv.org/abs/1803.06953
Repository Open Access

Konstantinos Dareiotis and Benjamin Gess: Supremum estimates for degenerate, quasilinear stochastic partial differential equations
In: Annales de l'Institut Henri Poincaré / B, 55 (2019) 3, p. 1765-1796
Bibtex DOI: 10.1214/18-AIHP934 ARXIV: https://arxiv.org/abs/1712.06655
Journal Open Access

Benjamin J. Fehrman and Benjamin Gess: Well-posedness of nonlinear diffusion equations with nonlinear, conservative noise
In: Archive for rational mechanics and analysis, 233 (2019) 1, p. 249-322
Bibtex DOI: 10.1007/s00205-019-01357-w ARXIV: https://arxiv.org/abs/1712.05775
Journal Open Access

Paul Gassiat and Benjamin Gess: Regularization by noise for stochastic Hamilton-Jacobi equations
In: Probability theory and related fields, 173 (2019) 3/4, p. 1063-1098
Bibtex DOI: 10.1007/s00440-018-0848-7 ARXIV: https://arxiv.org/abs/1609.07074
Repository Open Access

Benjamin Gess and Xavier Lamy: Regularity of solutions to scalar conservation laws with a force
In: Annales de l'Institut Henri Poincaré / C, 36 (2019) 2, p. 505-521
Bibtex DOI: 10.1016/j.anihpc.2018.07.002 ARXIV: https://arxiv.org/abs/1707.06866
Repository Open Access

Benjamin Gess and Scott A. Smith: Stochastic continuity equations with conservative noise
In: Journal de mathématiques pures et appliquées, 128 (2019), p. 225-263
Bibtex DOI: 10.1016/j.matpur.2019.02.002 ARXIV: https://arxiv.org/abs/1710.04906
Repository Open Access

Benjamin Gess and Martina Hofmanová: Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE
In: The annals of probability, 46 (2018) 5, p. 2495-2544
Bibtex DOI: 10.1214/17-AOP1231 ARXIV: https://arxiv.org/abs/1611.03600
Repository Open Access

Benjamin Gess and Mario Maurelli: Well-posedness by noise for scalar conservation laws
In: Communications in partial differential equations, 43 (2018) 12, p. 1702-1736
Bibtex DOI: 10.1080/03605302.2018.1535604 ARXIV: https://arxiv.org/abs/1701.05393
Repository Open Access

Franco Flandoli ; Benjamin Gess and Michael Scheutzow: Synchronization by noise
In: Probability theory and related fields, 168 (2017) 3/4, p. 511-556
Bibtex DOI: 10.1007/s00440-016-0716-2 ARXIV: http://arxiv.org/abs/1411.1340
Repository Open Access

Franco Flandoli ; Benjamin Gess and Michael Scheutzow: Synchronization by noise for order-preserving random dynamical systems
In: The annals of probability, 45 (2017) 2, p. 1325-1350
Bibtex DOI: 10.1214/16-AOP1088 ARXIV: http://arxiv.org/abs/1503.08737
Journal Open Access

Benjamin Gess and Michael Röckner: Stochastic variational inequalities and regularity for degenerate stochastic partial differential equations
In: Transactions of the American Mathematical Society, 369 (2017) 5, p. 3017-3045
Bibtex DOI: 10.1090/tran/6981 ARXIV: http://arxiv.org/abs/1405.5866
Repository Open Access

Benjamin Gess and Panagiotis E. Souganidis: Long-time behavior, invariant measures and regularizing effects for stochastic scalar conservation laws
In: Communications on pure and applied mathematics, 70 (2017) 8, p. 1562-1597
Bibtex DOI: 10.1002/cpa.21646 ARXIV: https://arxiv.org/abs/1411.3939
Repository Open Access

Benjamin Gess and Panagiotis E. Souganidis: Stochastic non-isotropic degenerate parabolic-hyperbolic equations
In: Stochastic processes and their applications, 127 (2017) 9, p. 2961-3004
Bibtex DOI: 10.1016/j.spa.2017.01.005 ARXIV: https://arxiv.org/abs/1611.01303
Repository Open Access

Peter K. Friz and Benjamin Gess: Stochastic scalar conservation laws driven by rough paths
In: Annales de l'Institut Henri Poincaré / C, 33 (2016) 4, p. 933-963
Bibtex DOI: 10.1016/j.anihpc.2015.01.009 ARXIV: http://arxiv.org/abs/1403.6785
Repository Open Access

Peter K. Friz ; Benjamin Gess ; Archil Gulisashvili and Sebastian Riedel: The Jain-Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theory
In: The annals of probability, 44 (2016) 1, p. 684-738
Bibtex DOI: 10.1214/14-AOP986 ARXIV: http://arxiv.org/abs/1307.3460
Repository Open Access

Paul Gassiat and Benjamin Gess: Regularization by noise for stochastic Hamilton-Jacobi equations [In: Rough paths, regularity structures and related topics ; 1 May - 7 May 2016 ; report no. 24/2016]
In: Oberwolfach reports, 13 (2016) 2, p. 1349-1353
Bibtex DOI: 10.4171/OWR/2016/24 LINK: https://publications.mfo.de/handle/mfo/3528
Repository Open Access

Benjamin Gess ; Benoît Perthame and Panagiotis E. Souganidis: Semi-discretization for stochastic scalar conservation laws with multiple rough fluxes
In: SIAM journal on numerical analysis, 54 (2016) 4, p. 2187-2209
Bibtex DOI: 10.1137/15M1053670 ARXIV: http://arxiv.org/abs/1512.06056
Repository Open Access

Benjamin Gess and Jonas M. Tölle: Ergodicity and local limits for stochastic local and nonlocal \(p\)-Laplace equations
In: SIAM journal on mathematical analysis, 48 (2016) 6, p. 4094-4125
Bibtex DOI: 10.1137/15M1049774 ARXIV: http://arxiv.org/abs/1507.04545
Repository Open Access

Benjamin Gess and Jonas M. Tölle: Stability of solutions to stochastic partial differential equations
In: Journal of differential equations, 260 (2016) 6, p. 4973-5025
Bibtex DOI: 10.1016/j.jde.2015.11.039 ARXIV: http://arxiv.org/abs/1506.01230
Repository Open Access

Michael Cranston ; Benjamin Gess and Michael Scheutzow: Weak synchronization for isotropic flows
In: Discrete and continuous dynamical systems / B, 21 (2015) 9, p. 3003-3014
Bibtex DOI: 10.3934/dcdsb.2016084 ARXIV: http://arxiv.org/abs/1510.09096
Repository Open Access

Benjamin Gess: Finite time extinction for stochastic sign fast diffusion and self-organized criticality
In: Communications in mathematical physics, 335 (2015) 1, p. 309-344
Bibtex DOI: 10.1007/s00220-014-2225-4 ARXIV: http://arxiv.org/abs/1310.6971
Repository Open Access

Benjamin Gess and Michael Röckner: Singular-degenerate multivalued stochastic fast diffusion equations
In: SIAM journal on mathematical analysis, 47 (2015) 5, p. 4058-4090
Bibtex DOI: 10.1137/151003726 ARXIV: http://arxiv.org/abs/1501.01544
Repository Open Access

Benjamin Gess and Panagiotis E. Souganidis: Scalar conservation laws with multiple rough fluxes
In: Communications in mathematical sciences, 13 (2015) 6, p. 1569-1597
Bibtex DOI: 10.4310/CMS.2015.v13.n6.a10 ARXIV: http://arxiv.org/abs/1406.2978
Repository Open Access

Benjamin Gess: Random attractors for stochastic porous media equations perturbed by space-time linear multiplicative noise
In: The annals of probability, 42 (2014) 2, p. 818-864
Bibtex DOI: 10.1214/13-AOP869 ARXIV: http://arxiv.org/abs/1108.2413
Repository Open Access

Benjamin Gess and Jonas M. Tölle: Multi-valued, singular stochastic evolution inclusions
In: Journal de mathématiques pures et appliquées, 101 (2014) 6, p. 789-827
Bibtex DOI: 10.1016/j.matpur.2013.10.004 ARXIV: http://arxiv.org/abs/1112.5672
Repository Open Access

Benjamin Gess: Finite speed of propagation for stochastic porous media equation
In: SIAM journal on mathematical analysis, 45 (2013) 5, p. 2734-2766
Bibtex DOI: 10.1137/120894713 ARXIV: http://arxiv.org/abs/1210.2415
Repository Open Access

Benjamin Gess: Random attractors for singular stochastic evolution equations
In: Journal of differential equations, 255 (2013) 3, p. 524-559
Bibtex DOI: 10.1016/j.jde.2013.04.023 ARXIV: http://arxiv.org/abs/1111.0205
Repository Open Access

Benjamin Gess: Random attractors for degenerate stochastic partial differential equations
In: Journal of dynamics and differential equations, 25 (2013) 1, p. 121-157
Bibtex DOI: 10.1007/s10884-013-9294-5 ARXIV: http://arxiv.org/abs/1206.2329
Repository Open Access

Benjamin Gess: Random attractors for stochastic porous media equations perturbed by space-time linear multiplicative noise
In: Comptes rendus mathematique, 350 (2012) 5-6, p. 299-302
Bibtex DOI: 10.1016/j.crma.2012.02.004 ARXIV: http://arxiv.org/abs/1108.2413
Repository Open Access

Benjamin Gess: Strong solutions for stochastic partial differential equations of gradient type
In: Journal of functional analysis, 263 (2012) 8, p. 2355-2383
Bibtex DOI: 10.1016/j.jfa.2012.07.001 ARXIV: http://arxiv.org/abs/1104.4243
Repository Open Access

Benjamin Gess ; Peter K. Friz ; Archil Gulisashvili and Sebastian Riedel: Spatial rough path lifts of stochastic convolutions [In: Rough paths and PDEs ; August 19-25th 2012 ; report no. 41/2012]
In: Oberwolfach reports, 9 (2012) 3, p. 2509-2513
Bibtex DOI: 10.4171/OWR/2012/41 LINK: https://publications.mfo.de/handle/mfo/3311
Repository Open Access

Benjamin Gess ; Wei Liu and Michael Röckner: Random attractors for a class of stochastic partial differential equations driven by general additive noise
In: Journal of differential equations, 251 (2011) 4-5, p. 1225-1253
Bibtex DOI: 10.1016/j.jde.2011.02.013 ARXIV: http://arxiv.org/abs/1010.4641
Repository Open Access

Wolf-Jürgen Beyn ; Benjamin Gess ; Paul Lescot and Michael Röckner: The global random attractor for a class of stochastic porous media equations
In: Communications in partial differential equations, 36 (2010) 3, p. 446-469
Bibtex DOI: 10.1080/03605302.2010.523919 ARXIV: http://arxiv.org/abs/1010.0551
Repository Open Access

Publications in Books and Conference Proceedings

Benjamin Gess: Regularization and well-posedness by noise for ordinary and partial differential equations
In: Stochastic partial differential equations and related fields : in honor of Michael Röckner, SPDERF, Bielefeld, Germany, October 10-14, 2016 / Andreas Eberle... (eds.)
Cham : Springer, 2018. - P. 43-67
(Springer proceedings in mathematics and statistics ; 229)
Bibtex DOI: 10.1007/978-3-319-74929-7_3 LINK: http://www.bgess.de/wp-content/uploads/Gess-Regularization-and-well-posedness-by-noise-for-ODE-and-PDE.pdf

Preprints

Benjamin J. Fehrman ; Benjamin Gess and Rishabh S. Gvalani: Ergodicity and random dynamical systems for conservative SPDEs
Repository Open Access

Paul Gassiat ; Benjamin Gess ; Pierre-Louis Lions and Panagiotis E. Souganidis: Long-time behaviour of stochastic Hamilton-Jacobi equations
Repository Open Access

Benjamin Gess ; Rishabh S. Gvalani and Vitalii Konarovskyi: Conservative SPDEs as fluctuating mean field limits of stochastic gradient descent
Repository Open Access

Benjamin Gess and Pavlos Tsatsoulis: Lyapunov exponents and synchronisation by noise for systems of SPDEs
Repository Open Access

L'ubomír Baňas ; Benjamin Gess and Marius Neuß: Stochastic partial differential equations arising in self-organized criticality
Repository Open Access

Benjamin Gess and Benjamin J. Fehrman: Well-posedness of the Dean-Kawasaki and the nonlinear Dawson-Watanabe equation with correlated noise
Repository Open Access

Benjamin Gess ; Rishabh S. Gvalani ; Florian Kunick and Felix Otto: Thermodynamically consistent and positivity-preserving discretization of the thin-film equation with thermal noise
Repository Open Access

Benjamin Gess and Ivan Yaroslavtsev: Stabilization by transport noise and enhanced dissipation in the Kraichnan model
Repository Open Access

L'ubomír Baňas ; Benjamin Gess and Christian Vieth: Numerical approximation of singular-degenerate parabolic stochastic PDEs
Repository Open Access

Nicolas Dirr ; Benjamin J. Fehrman and Benjamin Gess: Conservative stochastic PDE and fluctuations of the symmetric simple exclusion process
Repository Open Access

Benjamin J. Fehrman and Benjamin Gess: Non-equilibrium large deviations and parabolic-hyperbolic PDE with irregular drift
Repository Open Access

Peter K. Friz ; Benjamin Gess ; Archil Gulisashvili and Sebastian Riedel: Spatial rough path lifts of stochastic convolutions
Repository Open Access

Peter K. Friz ; Benjamin Gess and Sebastian Riedel: On the variational regularity of Cameron-Martin paths
Repository Open Access

Academic Theses

Benjamin Gess: Stochastic flows induced by stochastic partial differential equations
Dissertation, Universität Bielefeld, 2011
Bibtex

Benjamin Gess: Convexity of Chebyshev sets
Masterarbeit, Warwick University, 2009
Bibtex
29.11.2022, 06:30