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Research Group

Stochastic Partial Differential Equations

The research of this group concentrates on (nonlinear) stochastic partial differential equations (SPDE).

Portrait of Benjamin Gess
Research Group Leader

Benjamin Gess

Research Group Leader
Email - 954 F2 04
Stochastic Partial Differential Equations MiS Profile External Website
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Research

Our research centers around stochastic partial differential equations (SPDEs), nonlinear partial differential equations, stochastic dynamics, interacting particle systems, machine learning, fluid dynamics, with emphasis on conservative SPDEs.

Particular emphasis is laid upon:

  1. Regularization and well-posedness by noise
  2. Highly singular SPDE
  3. Stochastic dynamics

Members

Publications

inJournal
2024
Benjamin J. Fehrman et al.

Well-posedness of the Dean-Kawasaki and the nonlinear Dawson-Watanabe equation with correlated noise

In: Archive for rational mechanics and analysis

BibTex

 DOI: 10.1007/s00205-024-01963-3 ArXiv: 2108.08858
inJournal
2024
Paul Gassiat et al.

Long-time behavior of stochastic Hamilton-Jacobi equations

In: Journal of functional analysis

BibTex

 DOI: 10.1016/j.jfa.2023.110269 ArXiv: 2211.12099
Preprint
2024
Benjamin Gess et al.

Stochastic modified flows for Riemannian stochastic gradient descent

BibTex

 ArXiv: 2402.03467
inJournal
2024
Benjamin Gess et al.

Stochastic modified flows, mean-field limits and dynamics of stochastic gradient descent

In: Journal of machine learning research

BibTex

 ArXiv: 2302.07125 Link: www.jmlr.org
Preprint
2024
Benjamin Gess et al.

SVI solutions to stochastic nonlinear diffusion equations on general measure spaces

BibTex

 ArXiv: 2402.01479
inJournal
2023
L'ubomír Baňas et al.

Numerical approximation of singular-degenerate parabolic stochastic partial differential equations

In: IMA journal of numerical analysis

BibTex

 DOI: 10.1093/imanum/drad061 ArXiv: 2012.12150
inJournal
2023
Sebastian Becker et al.

Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations

In: Stochastics and partial differential equations : analysis and computations

BibTex

 DOI: 10.1007/s40072-021-00226-6 ArXiv: 1711.02423
inJournal
2023
Alex Blumenthal et al.

Exponential mixing for random dynamical systems and an example of Pierrehumbert

In: The annals of probability

BibTex

 DOI: 10.1214/23-AOP1627 ArXiv: 2204.13651
inJournal
2023
José Carrillo et al.

An invariance principle for gradient flows in the space of probability measures

In: Journal of differential equations

BibTex

 DOI: 10.1016/j.jde.2022.11.028 ArXiv: 2010.00424
Preprint
2023
Konstantinos Dareiotis et al.

Solutions to the stochastic thin-film equation for initial values with non-full support

BibTex

 ArXiv: 2305.06017
inJournal
2023
Matias G. Delgadino et al.

Phase transitions, logarithmic Sobolev inequalities, and uniform-in-time propagation of chaos for weakly interacting diffusions

In: Communications in mathematical physics

BibTex

 DOI: 10.1007/s00220-023-04659-z ArXiv: 2112.06304
inJournal
2023
Joscha Diehl et al.

The moving-frame method for iterated-integrals signature : orthogonal invariants

In: Foundations of computational mathematics

BibTex

 DOI: 10.1007/s10208-022-09569-5 ArXiv: 2012.05880
All Group Publications
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AG Analysis-Probability

Metastability of cubic nonlinear wave equation

  • Petri Laarne (University of Helsinki)
E2 10 (Leon-Lichtenstein)

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AG Analysis-Probability

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  • Annika Burmester (University of Bielefeld)
E1 05 (Leibniz-Saal)

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AG Analysis-Probability

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  • Christian Wagner (MPI MiS, Leipzig)
A3 01 (Sophus-Lie room)

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OS Analysis-Probability

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  • Barbara Verfürth (Universität Bonn)
G3 10 (Lecture hall)

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OS Analysis-Probability

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  • Lisa Hartung (Universität Mainz)
G3 10 (Lecture hall)

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AG Analysis-Probability

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  • Immanuel Zachhuber (FU Berlin)
E1 05 (Leibniz-Saal)

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AG Analysis-Probability

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  • Da Li (FU Berlin)
E1 05 (Leibniz-Saal)

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AG Analysis-Probability

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  • Olga Shishkina (MPI for Dynamics and Self-Organization, Göttingen)
E1 05 (Leibniz-Saal)

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OS Analysis-Probability

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  • Vadim Gorin (University of California, Berkeley)
E1 05 (Leibniz-Saal)

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OS Analysis-Probability

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  • Paul Dario (Université Paris Est Créteil)
E1 05 (Leibniz-Saal)

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OS Analysis-Probability

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  • Michael Loss (Georgia Institute of Technology)
A3 01 (Sophus-Lie room)

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OS Analysis-Probability

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  • Tomasz Komorowski (Polish Academy of Sciences)
E1 05 (Leibniz-Saal)

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