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


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

Summary:

The aim of the project is to further extend the theory of Fokker-Planck-Kolmogorov equations oriented towards new applications with emphasis on passing to general state spaces, including besides infinite dimensional linear spaces, in particular, infinite dimensional manifolds, configuration spaces and finally also general metric measure spaces. The intrinsic feature of our approach is to formulate a Fokker-Planck Kolmogorov equation as a partial differential equation on measures, i.e. solutions are paths of (probability) measures. This is most natural and necessary on general state spaces since there is no intrinsic reference measure available on such spaces. The project consists of three parts: (I) Fokker--Planck--Kolmogorov equations and weak uniqueness of stochastic partial differential equations; (II) Degenerate local and nonlocal Fokker-Planck-Kolmogorov equations; (III) Nonlinear Fokker-Planck-Kolmogorov equations.


Recent Preprints:

20049 Viorel Barbu, Michael Röckner PDF

Solutions for nonlinear Fokker-Planck equations with measures as initial data and McKean-Vlasov equations

Project: A5

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Solutions for nonlinear Fokker-Planck equations with measures as initial data and McKean-Vlasov equations


Authors: Viorel Barbu, Michael Röckner Projects: A5
Submission Date: 05.05.2020 Submitter: Alexander Grigor'yan
Download: PDF Link: 20049

20011 Alexander Shaposhnikov, Lukas Wresch PDF

Pathwise vs. Path-by-Path Uniqueness

Project: A5, B1

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Pathwise vs. Path-by-Path Uniqueness


Authors: Alexander Shaposhnikov, Lukas Wresch Projects: A5, B1
Submission Date: 23.01.2020 Submitter: Michael Röckner
Download: PDF Link: 20011

19103 Yuri Kozitsky, Michael Röckner PDF

A Markov process for an infinite interacting particle system in the continuum

Project: A5, B1

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A Markov process for an infinite interacting particle system in the continuum


Authors: Yuri Kozitsky, Michael Röckner Projects: A5, B1
Submission Date: 04.12.2019 Submitter: Martina Hofmanová
Download: PDF Link: 19103

19096 Michael Röckner, Longjie Xie, Xicheng Zhang PDF

Superposition principle for non-local Fokker-Planck operators

Project: A5, B1

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Superposition principle for non-local Fokker-Planck operators


Authors: Michael Röckner, Longjie Xie, Xicheng Zhang Projects: A5, B1
Submission Date: 25.10.2019 Submitter: Alexander Grigor'yan
Download: PDF Link: 19096

19073 Anna N. Doledenok PDF

On Kantorovich multimarginal optimal transportation problems with density constraints

Project: A5

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On Kantorovich multimarginal optimal transportation problems with density constraints


Authors: Anna N. Doledenok Projects: A5
Submission Date: 27.09.2019 Submitter: Michael Röckner
Download: PDF Link: 19073

19070 Viorel Barbu, Michael Röckner PDF

Uniqueness for nonlinear Fokker-Planck equations and weak uniqueness for McKean-Vlasov SDEs

Project: A5

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Uniqueness for nonlinear Fokker-Planck equations and weak uniqueness for McKean-Vlasov SDEs


Authors: Viorel Barbu, Michael Röckner Projects: A5
Submission Date: 10.09.2019 Submitter: Alexander Grigor'yan
Download: PDF Link: 19070

19027 Vladimir Bogachev, Michael Röckner, Stanislav Shaposhnikov PDF

On convergence to stationary distributions for solutions of nonlinear Fokker–Planck–Kolmogorov equations

Project: A5

Published: J. Math. Sci (1), no. 242 (2019), 69-84

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On convergence to stationary distributions for solutions of nonlinear Fokker–Planck–Kolmogorov equations


Authors: Vladimir Bogachev, Michael Röckner, Stanislav Shaposhnikov Projects: A5
Submission Date: 27.05.2019 Submitter: Alexander Grigor'yan
Download: PDF Link: 19027
Published: J. Math. Sci (1), no. 242 (2019), 69-84

19020 Panpan Ren, Michael Röckner, Feng-Yu Wang PDF

Linearization of Nonlinear Fokker-Planck Equations and Applications

Project: A5

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Linearization of Nonlinear Fokker-Planck Equations and Applications


Authors: Panpan Ren, Michael Röckner, Feng-Yu Wang Projects: A5
Submission Date: 18.05.2019 Submitter: Alexander Grigor'yan
Download: PDF Link: 19020

19013 Feng-Yu Wang PDF

Diffusions and PDEs on Wasserstein Space

Project: A5

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Diffusions and PDEs on Wasserstein Space


Authors: Feng-Yu Wang Projects: A5
Submission Date: 11.04.2019 Submitter: Michael Röckner
Download: PDF Link: 19013

19012 Viorel Barbu, Michael Röckner PDF

The evolution to equilibrium of solutions to nonlinear Fokker-Planck equation

Project: A5

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The evolution to equilibrium of solutions to nonlinear Fokker-Planck equation


Authors: Viorel Barbu, Michael Röckner Projects: A5
Submission Date: 10.04.2019 Submitter: Alexander Grigor'yan
Download: PDF Link: 19012



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