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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:

20091 Martin Dieckmann PDF

A Restricted Superposition Principle for (non-)linear Fokker–Planck–Kolmogorov Equations on Hilbert Spaces

Project: A5, B1

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A Restricted Superposition Principle for (non-)linear Fokker–Planck–Kolmogorov Equations on Hilbert Spaces


Authors: Martin Dieckmann Projects: A5, B1
Submission Date: 06.08.2020 Submitter: Michael Röckner
Download: PDF Link: 20091

20090 Zimo Hao, Michael Röckner, Xicheng Zhang PDF

Euler Scheme for Density Dependent Stochastic Differential Equations

Project: A5, B1

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Euler Scheme for Density Dependent Stochastic Differential Equations


Authors: Zimo Hao, Michael Röckner, Xicheng Zhang Projects: A5, B1
Submission Date: 31.07.2020 Submitter: Alexander Grigor'yan
Download: PDF Link: 20090

20072 Jianhai Bao, Panpan Ren, Feng-Yu Wang PDF

Bismut Formula for Lions Derivative of Distribution-Path Dependent SDEs

Project: A5

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Bismut Formula for Lions Derivative of Distribution-Path Dependent SDEs


Authors: Jianhai Bao, Panpan Ren, Feng-Yu Wang Projects: A5
Submission Date: 01.07.2020 Submitter: Michael Röckner
Download: PDF Link: 20072

20071 Xing Huang, Feng-Yu Wang PDF

Derivative Estimates on Distributions of McKean-Vlasov SDEs

Project: A5

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Derivative Estimates on Distributions of McKean-Vlasov SDEs


Authors: Xing Huang, Feng-Yu Wang Projects: A5
Submission Date: 01.07.2020 Submitter: Michael Röckner
Download: PDF Link: 20071

20070 Panpan Ren, Feng-Yu Wang PDF

Donsker-Varadhan Large Deviations for Path-Distribution Dependent SPDEs

Project: A5

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Donsker-Varadhan Large Deviations for Path-Distribution Dependent SPDEs


Authors: Panpan Ren, Feng-Yu Wang Projects: A5
Submission Date: 01.07.2020 Submitter: Michael Röckner
Download: PDF Link: 20070

20069 Feng-Yu Wang PDF

Convergence in Wasserstein Distance for Empirical Measures of Dirichlet Diffusion Processes on Manifolds

Project: A5

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Convergence in Wasserstein Distance for Empirical Measures of Dirichlet Diffusion Processes on Manifolds


Authors: Feng-Yu Wang Projects: A5
Submission Date: 01.07.2020 Submitter: Michael Röckner
Download: PDF Link: 20069

20068 Feng-Yu Wang PDF

Precise Limit in Wasserstein Distance for Conditional Empirical Measures of Dirichlet Diffusion Processes

Project: A5

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Precise Limit in Wasserstein Distance for Conditional Empirical Measures of Dirichlet Diffusion Processes


Authors: Feng-Yu Wang Projects: A5
Submission Date: 01.07.2020 Submitter: Michael Röckner
Download: PDF Link: 20068

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



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