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



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:

19027 Vladimir Bogachev, Michael Röckner, Stanislav Shaposhnikov PDF

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

Project: A5

To appear: J. Math. Sci (2019)

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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
To appear: J. Math. Sci (2019)

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

Ergodicity and Feynman-Kac Formula for Space-Distribution Valued Diffusion Processes

Project: A5

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Ergodicity and Feynman-Kac Formula for Space-Distribution Valued Diffusion Processes


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

19006 Vladimir Bogachev, Michael Röckner, Stanislav Shaposhnikov PDF

On the Ambrosio–Figalli–Trevisan superposition principle for probability solutions to Fokker–Planck–Kolmogorov equations

Project: A5

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On the Ambrosio–Figalli–Trevisan superposition principle for probability solutions to Fokker–Planck–Kolmogorov equations


Authors: Vladimir Bogachev, Michael Röckner, Stanislav Shaposhnikov Projects: A5
Submission Date: 28.03.2019 Submitter: Alexander Grigor'yan
Download: PDF Link: 19006

18074 Egor D. Kosov PDF

Total variation distance estimates via $L^2$-norm for polynomials in log-concave random vectors

Project: A5

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Total variation distance estimates via $L^2$-norm for polynomials in log-concave random vectors


Authors: Egor D. Kosov Projects: A5
Submission Date: 20.12.2018 Submitter: Michael Röckner
Download: PDF Link: 18074

18073 Jianhai Bao, Feng-Yu Wang, Chenggui Yuan PDF

Asymptotic Log-Harnack Inequality and Applications for Stochastic Systems of Infinite Memory

Project: A5

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Asymptotic Log-Harnack Inequality and Applications for Stochastic Systems of Infinite Memory


Authors: Jianhai Bao, Feng-Yu Wang, Chenggui Yuan Projects: A5
Submission Date: 17.12.2018 Submitter: Xiangchan Zhu
Download: PDF Link: 18073

18053 Michael Röckner, Viorel Barbu PDF

From nonlinear Fokker-Planck equations to solutions of distribution dependent SDE

Project: A5

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From nonlinear Fokker-Planck equations to solutions of distribution dependent SDE


Authors: Michael Röckner, Viorel Barbu Projects: A5
Submission Date: 08.11.2018 Submitter: Alexander Grigor'yan
Download: PDF Link: 18053

18052 Panpan Ren, Feng-Yu Wang PDF

Bismut Formula for Lions Derivative of Distribution Dependent SDEs and Applications

Project: A5

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Bismut Formula for Lions Derivative of Distribution Dependent SDEs and Applications


Authors: Panpan Ren, Feng-Yu Wang Projects: A5
Submission Date: 07.11.2018 Submitter: Michael Röckner
Download: PDF Link: 18052

18050 Xicheng Zhang, Michael Röckner PDF

Well-posedness of distribution dependent SDEs with singular drifts

Project: A5, B1

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Well-posedness of distribution dependent SDEs with singular drifts


Authors: Xicheng Zhang, Michael Röckner Projects: A5, B1
Submission Date: 06.11.2018 Submitter: Friedrich Götze
Download: PDF Link: 18050



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