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Project A5: Fokker-Planck-Kolmogorov equations on general state spaces


Principal Investigator(s)
Michael Röckner
Feng-Yu Wang
Investigator(s)
Walter Hoh
Visitor(s)
Currently no visitors.

Summary:

The aim of Project A5 is to further extend the theory of Fokker–Planck–Kolmogorov equations (FPKEs) oriented towards new applications. The emphasis on the purely analytic side is on the geometry of FPKEs, their connection to optimal transport problems, their asymptotic behavior and non-local variants of them. On the stochastic analytic side the emphasis is on nonlinear FPKEs and their probabilistic counterparts, namely nonlinear Markov processes. The research of Project A5 is structured in the following four parts: (I) Geometry of nonlinear FPKEs and connections to the Monge–Kantorovich optimal transport problem; (II) Asymptotic analysis for nonlinear FPKEs; (III) Time-fractional non-local non-linear FPKEs; (IV) Nonlinear FPKEs and nonlinear Markov process.


Recent Preprints:

25026 Adrian Padellaro, Sanjaye Ramgoolam, Rak-Kyeong Seong PDF

Row and column detection complexities ofcharacter tables

Project: A5, C6

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Row and column detection complexities ofcharacter tables


Authors: Adrian Padellaro, Sanjaye Ramgoolam, Rak-Kyeong Seong Projects: A5, C6
Submission Date: 14.03.2025 Submitter: Gernot Akemann
Download: PDF Link: 25026

25015 Michael Röckner, Viorel Barbu PDF

Nonlinear Fokker–Planck equations as smooth Hilbertian gradient flows

Project: A5

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Nonlinear Fokker–Planck equations as smooth Hilbertian gradient flows


Authors: Michael Röckner, Viorel Barbu Projects: A5
Submission Date: 03.03.2025 Submitter: Matthias Erbar
Download: PDF Link: 25015

25002 Vladimir Bogachev, Tikhon Krasovitskiy, Michael Röckner, Francesco Russo, Stanislav Shaposhnikov PDF

The superposition principle for solutions to Fokker-Planck-Kolmogorov equations with potential terms

Project: A5

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The superposition principle for solutions to Fokker-Planck-Kolmogorov equations with potential terms


Authors: Vladimir Bogachev, Tikhon Krasovitskiy, Michael Röckner, Francesco Russo, Stanislav Shaposhnikov Projects: A5
Submission Date: 16.01.2025 Submitter: Alexander Grigor'yan
Download: PDF Link: 25002

25001 Vladimir Bogachev, Tikhon Krasovitskiy, Michael Röckner, Stanislav Shaposhnikov PDF

Asymptotic behaviour of solutions to Fokker-Planck-Kolmogorov equations

Project: A5

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Asymptotic behaviour of solutions to Fokker-Planck-Kolmogorov equations


Authors: Vladimir Bogachev, Tikhon Krasovitskiy, Michael Röckner, Stanislav Shaposhnikov Projects: A5
Submission Date: 16.01.2025 Submitter: Alexander Grigor'yan
Download: PDF Link: 25001

24128 PDF

Strong solutions to degenerate SDEs and uniqueness for degenerate Fokker-Planck equations

Project: A5

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Strong solutions to degenerate SDEs and uniqueness for degenerate Fokker-Planck equations


Authors: Projects: A5
Submission Date: 07.04.2025 Submitter: Michael Röckner
Download: PDF Link: 24128

24118 Lucian Beznea, Iulian Cimpean, Michael Röckner PDF

Construction of Hunt processes by the Lyapunov method and applications to generalized Mehler semigroups

Project: A5

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Construction of Hunt processes by the Lyapunov method and applications to generalized Mehler semigroups


Authors: Lucian Beznea, Iulian Cimpean, Michael Röckner Projects: A5
Submission Date: 11.03.2025 Submitter: Moritz Kaßmann
Download: PDF Link: 24118

24117 Chongyang Ren, Xicheng Zhang PDF

Heat kernel estimates for kinetic SDEs with drifts being unbounded and in Kato's class

Project: A5

Published: Bernoulli 31, no. 2 (2025), 1402–1427

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Heat kernel estimates for kinetic SDEs with drifts being unbounded and in Kato's class


Authors: Chongyang Ren, Xicheng Zhang Projects: A5
Submission Date: 14.03.2025 Submitter: Michael Röckner
Download: PDF Link: 24117
Published: Bernoulli 31, no. 2 (2025), 1402–1427

24114 Haojie Hou, Xicheng Zhang PDF

Heat kernel estimates for nonlocal kinetic operators

Project: A5

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Heat kernel estimates for nonlocal kinetic operators


Authors: Haojie Hou, Xicheng Zhang Projects: A5
Submission Date: 14.03.2025 Submitter: Michael Röckner
Download: PDF Link: 24114

24093 Yuri Kozitsky, Michael Röckner PDF

The stochastic evolution of an infinite population with logistic-type interaction

Project: A5

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The stochastic evolution of an infinite population with logistic-type interaction


Authors: Yuri Kozitsky, Michael Röckner Projects: A5
Submission Date: 02.12.2024 Submitter: Ellen Baake
Download: PDF Link: 24093

24075 Viorel Barbu, Marco Rehmeier, Michael Röckner PDF

$p$-Brownian motion and the $p$-Laplacian

Project: A5, B1

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$p$-Brownian motion and the $p$-Laplacian


Authors: Viorel Barbu, Marco Rehmeier, Michael Röckner Projects: A5, B1
Submission Date: 04.10.2024 Submitter: Alexander Grigor'yan
Download: PDF Link: 24075


All Publications of this Project


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