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Workshop

Equilibria of nonlinear distorted Brownian motions

  • Michael Röckner (University of Bielefeld)
E1 05 (Leibniz-Saal)

Abstract

Joint work with: Viorel Barbu (Romanian Academy, Iasi)

This talk will review the connection of nonlinear Fokker-Planck-Kolmogorov (FPK) equations and McKean-Vlasov SDEs, with special emphasis on the case where the coefficients depend Nemytskii-type on the time marginal laws. A class of examples are nonlinear distorted Brownian motions. Recent results on their asymptotic behaviour, obtained through their corresponding nonlinear FPK equations, will be presented both in the non-degenerate and degenerate case.

References
Barbu, Viorel; Röckner, Michael Probabilistic representation for solutions to nonlinear Fokker-Planck equations. SIAM J. Math. Anal. 50 (2018), no. 4, 4246–4260.
Barbu, Viorel; Röckner, Michael From nonlinear Fokker-Planck equations to solutions of distribution dependent SDE. Ann. Probab. 48 (2020), no. 4, 1902–1920.
Barbu, Viorel; Röckner, Michael Solutions for nonlinear Fokker-Planck equations with measures as initial data and McKean-Vlasov equations. J. Funct. Anal. 280 (2021), no. 7, 108926, 35 pp.
Barbu, Viorel; Röckner, Michael The invariance principle for nonlinear Fokker-Planck equations. J. Differential Equations 315 (2022), 200–221.
Barbu, Viorel, Röckner, Michael Uniqueness for nonlinear Fokker-Planck equations and for McKean-Vlasov SDEs: The degenerate case arXiv:2203.00122
Barbu, Viorel, Röckner, Michael The evolution to equilibrium of solutions to nonlinear Fokker-Planck equations arXiv:1904.08291 , to appear in Indiana Univ. Math. J., 36 pp. 


Links

conference
16.05.22 25.05.22

Mathematical Concepts in the Sciences and Humanities

MPI für Mathematik in den Naturwissenschaften Leipzig (Leipzig) E1 05 (Leibniz-Saal) Live Stream

Katharina Matschke

Max Planck Institute for Mathematics in the Sciences, Germany Contact via Mail

Nihat Ay

Hamburg University of Technology, Germany and Santa Fe Institute

Eckehard Olbrich

Max Planck Institute for Mathematics in the Sciences, Germany

Felix Otto

Max Planck Institute for Mathematics in the Sciences, Germany

Bernd Sturmfels

Max Planck Institute for Mathematics in the Sciences, Germany