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2026
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Ergodicity for SPDEs driven by divergence-free transport noise
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2026
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Large spikes in stochastic gradient descent : a large-deviations view
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2026
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Probabilistically strong solutions to stochastic Euler equations
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2026
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The porous medium equation : multiscale integrability in large deviations
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2026
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Conservative stochastic PDE and fluctuations of the symmetric simple exclusion process
In: Communications in mathematical physics, 407 (2026) 4, p. 74inJournal
2026
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Conservative stochastic PDEs on the whole space
In: Stochastics and partial differential equations : analysis and computations, 14 (2026) 1, pp. 350-388inJournal
2026
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Existence of martingale solutions to a stochastic kinetic model of chemotaxis
In: Nonlinear differential equations and applications, 33 (2026) 2, p. 52inJournal
2026
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Exponential convergence rates for momentum stochastic gradient descent in the overparametrized setting
In: Mathematical programming, (2026)inJournal
2026
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Higher order fluctuation expansions for nonlinear stochastic heat equations in singular limits
In: Stochastic processes and their applications, 193 (2026), p. 104847inJournal
2026
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Low temperature expansion for the Euclidean \(\Phi^4_2\)-measure
In: Transactions of the American Mathematical Society, (2026)inJournal
2026
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Solutions to the stochastic thin-film equation for initial values with non-full support
In: Transactions of the American Mathematical Society, 379 (2026) 4, pp. 2343-2383Preprint
2025
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Matching large deviation bounds of the zero-range process in the whole space
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2025
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Conservative SPDEs as fluctuating mean field limits of stochastic gradient descent
In: Probability theory and related fields, 192 (2025) 3/4, pp. 1447-1515Preprint
2025
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Random dynamical systems for McKean-Vlasov SDEs via rough path theory
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2025
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Stabilization by transport noise and enhanced dissipation in the Kraichnan model
In: Journal of evolution equations, 25 (2025) 2, p. 42inJournal
2025
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Stochastic partial differential equations arising in self-organized criticality
In: The annals of applied probability, 35 (2025) 1, pp. 481-522inJournal
2025
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The porous medium equation : large deviations and gradient flow with degenerate and unbounded diffusion
In: Communications on pure and applied mathematics, 78 (2025) 9, pp. 1609-1655Preprint
2025
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THINNs : thermodynamically informed neural networks
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2024
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A quantitative central limit theorem for the simple symmetric exclusion process
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2024
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Long-time behavior of stochastic Hamilton-Jacobi equations
In: Journal of functional analysis, 286 (2024) 4, p. 110269inJournal
2024
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Lyapunov exponents and synchronisation by noise for systems of SPDEs
In: The annals of probability, 52 (2024) 5, pp. 1903-1953inJournal
2024
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Numerical approximation of singular-degenerate parabolic stochastic partial differential equations
In: IMA journal of numerical analysis, 44 (2024) 4, pp. 2090-2137inJournal
2024
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Stochastic modified flows for Riemannian stochastic gradient descent
In: SIAM journal on control and optimization, 62 (2024) 6, pp. 3288-3314inJournal
2024
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Stochastic modified flows, mean-field limits and dynamics of stochastic gradient descent
In: Journal of machine learning research, 25 (2024) 30, pp. 1-27inJournal
2024
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SVI solutions to stochastic nonlinear diffusion equations on general measure spaces
In: Journal of evolution equations, 24 (2024) 4, p. 94inJournal
2024
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Well-posedness of the Dean-Kawasaki and the nonlinear Dawson-Watanabe equation with correlated noise
In: Archive for rational mechanics and analysis, 248 (2024) 2, p. 20Preprint
2023
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Landau-Lifshitz-Navier-Stokes equations : large deviations and relationship to the energy equality
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2023
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Non-equilibrium large deviations and parabolic-hyperbolic PDE with irregular drift
In: Inventiones mathematicae, 234 (2023) 2, pp. 573-636Preprint
2023
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Optimal regularity in time and space for nonlocal porous medium type equations
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2023
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Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations
In: Stochastics and partial differential equations : analysis and computations, 11 (2023) 1, pp. 211-268inJournal
2023
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Thermodynamically consistent and positivity-preserving discretization of the thin-film equation with thermal noise
In: Mathematics of computation, 92 (2023), pp. 1931-1976inJournal
2022
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An example of intrinsic randomness in deterministic PDEs
In: Stochastics and dynamics, 22 (2022) 7, p. 2240023Preprint
2022
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Ergodicity and random dynamical systems for conservative SPDEs
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2022
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Optimal regularity in time and space for stochastic porous medium equations
In: The annals of probability, 50 (2022) 6, pp. 2288-2343inJournal
2021
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Non-negative martingale solutions to the stochastic thin-film equation with nonlinear gradient noise
In: Archive for rational mechanics and analysis, 242 (2021) 1, pp. 179-234inJournal
2021
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Optimal regularity for the porous medium equation
In: Journal of the European Mathematical Society, 23 (2021) 2, pp. 425-465inJournal
2021
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Path-by-path well-posedness of nonlinear diffusion equations with multiplicative noise
In: Journal de mathématiques pures et appliquées, 148 (2021), pp. 221-266inJournal
2021
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Porous media equations with multiplicative space-time white noise
In: Annales de l'Institut Henri Poincaré / B : Probabilites et statistiques, 57 (2021) 4, pp. 2354-2371inJournal
2020
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Convergence rates for the stochastic gradient descent method for non-convex objective functions
In: Journal of machine learning research, 21 (2020) 136, pp. 1-48inJournal
2020
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Density bounds for solutions to differential equations driven by Gaussian rough paths
In: Journal of theoretical probability, 33 (2020) 2, pp. 611-648inJournal
2020
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Ergodicity for stochastic porous media equations with multiplicative noise
In: SIAM journal on mathematical analysis, 52 (2020) 5, pp. 4524-4564inJournal
2020
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Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations
In: BIT : numerical mathematics, 60 (2020) 4, pp. 1057-1073inJournal
2020
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Nonlinear diffusion equations with nonlinear gradient noise
In: Electronic journal of probability, 25 (2020), p. 35inJournal
2020
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Optimal regularity in time and space for the porous medium equation
In: Analysis and PDE, 13 (2020) 8, pp. 2441-2480inJournal
2020
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Random attractors for locally monotone stochastic partial differential equations
In: Journal of differential equations, 269 (2020) 4, pp. 3414-3455inJournal
2020
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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, pp. 421-448inJournal
2020
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Synchronization by noise for the stochastic quantization equation in dimensions \(2\) and \(3\)
In: Stochastics and dynamics, 20 (2020) 6, p. 240006inJournal
2020
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The stochastic thin-film equation : existence of nonnegative martingale solutions
In: Stochastic processes and their applications, 130 (2020) 12, pp. 7260-7302inJournal
2019
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Entropy solutions for stochastic porous media equations
In: Journal of differential equations, 266 (2019) 6, pp. 3732-3763inJournal
2019
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Path-by-path regularization by noise for scalar conservation laws
In: Journal of functional analysis, 277 (2019) 5, pp. 1469-1498inJournal
2019
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Regularity of solutions to scalar conservation laws with a force
In: Annales de l'Institut Henri Poincaré / C, 36 (2019) 2, pp. 505-521inJournal
2019
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Regularization by noise for stochastic Hamilton-Jacobi equations
In: Probability theory and related fields, 173 (2019) 3/4, pp. 1063-1098inJournal
2019
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Stochastic continuity equations with conservative noise
In: Journal de mathématiques pures et appliquées, 128 (2019), pp. 225-263inJournal
2019
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Stochastic nonlinear Fokker-Planck equations
In: Nonlinear analysis / A, 187 (2019), pp. 259-278inJournal
2019
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Supremum estimates for degenerate, quasilinear stochastic partial differential equations
In: Annales de l'Institut Henri Poincaré / B : Probabilites et statistiques, 55 (2019) 3, pp. 1765-1796inJournal
2019
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Well-posedness of nonlinear diffusion equations with nonlinear, conservative noise
In: Archive for rational mechanics and analysis, 233 (2019) 1, pp. 249-322inBook
2018
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. - pp. 43-67
(Springer proceedings in mathematics and statistics ; 229)
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2018
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Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE
In: The annals of probability, 46 (2018) 5, pp. 2495-2544inJournal
2018
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Well-posedness by noise for scalar conservation laws
In: Communications in partial differential equations, 43 (2018) 12, pp. 1702-1736inJournal
2017
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Long-time behavior, invariant measures and regularizing effects for stochastic scalar conservation laws
In: Communications on pure and applied mathematics, 70 (2017) 8, pp. 1562-1597inJournal
2017
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Stochastic non-isotropic degenerate parabolic-hyperbolic equations
In: Stochastic processes and their applications, 127 (2017) 9, pp. 2961-3004inJournal
2017
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Stochastic variational inequalities and regularity for degenerate stochastic partial differential equations
In: Transactions of the American Mathematical Society, 369 (2017) 5, pp. 3017-3045inJournal
2017
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Synchronization by noise
In: Probability theory and related fields, 168 (2017) 3/4, pp. 511-556inJournal
2017
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Synchronization by noise for order-preserving random dynamical systems
In: The annals of probability, 45 (2017) 2, pp. 1325-1350inJournal
2016
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Ergodicity and local limits for stochastic local and nonlocal \(p\)-Laplace equations
In: SIAM journal on mathematical analysis, 48 (2016) 6, pp. 4094-4125inJournal
2016
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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, pp. 1349-1353inJournal
2016
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Semi-discretization for stochastic scalar conservation laws with multiple rough fluxes
In: SIAM journal on numerical analysis, 54 (2016) 4, pp. 2187-2209inJournal
2016
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Stability of solutions to stochastic partial differential equations
In: Journal of differential equations, 260 (2016) 6, pp. 4973-5025inJournal
2016
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Stochastic scalar conservation laws driven by rough paths
In: Annales de l'Institut Henri Poincaré / C, 33 (2016) 4, pp. 933-963inJournal
2016
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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, pp. 684-738inJournal
2015
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Finite time extinction for stochastic sign fast diffusion and self-organized criticality
In: Communications in mathematical physics, 335 (2015) 1, pp. 309-344inJournal
2015
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Scalar conservation laws with multiple rough fluxes
In: Communications in mathematical sciences, 13 (2015) 6, pp. 1569-1597inJournal
2015
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Singular-degenerate multivalued stochastic fast diffusion equations
In: SIAM journal on mathematical analysis, 47 (2015) 5, pp. 4058-4090inJournal
2015
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Weak synchronization for isotropic flows
In: Discrete and continuous dynamical systems / B, 21 (2015) 9, pp. 3003-3014inJournal
2014
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Multi-valued, singular stochastic evolution inclusions
In: Journal de mathématiques pures et appliquées, 101 (2014) 6, pp. 789-827inJournal
2014
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Random attractors for stochastic porous media equations perturbed by space-time linear multiplicative noise
In: The annals of probability, 42 (2014) 2, pp. 818-864inJournal
2013
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Finite speed of propagation for stochastic porous media equation
In: SIAM journal on mathematical analysis, 45 (2013) 5, pp. 2734-2766Preprint
2013
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On the variational regularity of Cameron-Martin paths
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2013
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Random attractors for degenerate stochastic partial differential equations
In: Journal of dynamics and differential equations, 25 (2013) 1, pp. 121-157inJournal
2013
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Random attractors for singular stochastic evolution equations
In: Journal of differential equations, 255 (2013) 3, pp. 524-559Preprint
2013
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Spatial rough path lifts of stochastic convolutions
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2012
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Random attractors for stochastic porous media equations perturbed by space-time linear multiplicative noise
In: Comptes rendus mathematique, 350 (2012) 5-6, pp. 299-302inJournal
2012
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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, pp. 2509-2513inJournal
2012
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Strong solutions for stochastic partial differential equations of gradient type
In: Journal of functional analysis, 263 (2012) 8, pp. 2355-2383inJournal
2011
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Random attractors for a class of stochastic partial differential equations driven by general additive noise
In: Journal of differential equations, 251 (2011) 4-5, pp. 1225-1253Academic
2011
Stochastic flows induced by stochastic partial differential equations
Dissertation, Universität Bielefeld, 2011inJournal
2010
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The global random attractor for a class of stochastic porous media equations
In: Communications in partial differential equations, 36 (2010) 3, pp. 446-469Academic
2009