Nonlinear Fokker–Planck equations with fractional Laplacian and McKean–Vlasov SDEs with L ́evy–Noise

Date: 

Friday, 26 July, 2024 - 15:00 to 16:00

Speaker : Michael Röckner, Bielefeld University, Germany

Time : 15:00 - 16:00 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

Zoom : A link will appear here, an hour before the talk.

Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords: Nonlinear Fokker-Planck equation, fractional Laplacian, nonlinear Markov process, McKean-Vlasov SDE, Levy noise

Abstract: This talk is concerned with the existence of mild solutions to nonlinear Fokker–Planck equations with fractional Laplace operator (−∆)s  for s ∈ ( 0.5 , 1). The uniqueness of Schwartz distributional solutions is also proved under suitable assumptions on diffusion and drift terms. As applications, weak existence and uniqueness of soultions to McKean–Vlasov equations with Lèvy–Noise, as well as the Markov property for their laws are proved.

Biography: Michael Röckner is a Professor of Mathematics at Bielefeld University. He has had previous professorial positions at Purdue University and the University of Bonn and was a Reader at the University of Edinburgh. He received his Doctor Degree and his Habilitation from Bielefeld University. He won the Sir Edmund Whittaker Memorial Prize, the Heinz Mayer Leibnitz Prize and the Max Planck Research Prize. In 2017 he was awarded an honorary Dr. of Science degree by the University of Swansea. He is a Distinguished Visiting Professor at the Academy of Mathematics and Systems Science in Beijing and won the Award for International Cooperation of the Chinese Academy of Sciences in 2023. On June 24, 2024, he received the International Science and Technology Cooperation Award of the People’s Republic of China. He is a member of the Academia Europaea, the Academy of Science and Literature, Mainz, and a foreign honorary member of the Romanian Academy of Sciences.

He was the President of the German Mathematical Society (DMV) and the Director of the Centre for Interdisciplinary Reseach (ZiF) in Bielefeld. He served as a panel chair for the Advanced Grants of the European Research Council, as a member of the Selection Committee for the Senior Humboldt Awards, as a member of the Senate’s Commission for Collaborative Research Centers of the German Science Foundation (DFG) and for 11 years as the Dekan of Bielefeld University’s Faculty of Mathematics.

Apart from six books he has published close to 400 research articles, supervised 31 PhD students and was host for 10 Humboldt scholars. His main field of research is Stochastic Analysis.

Bibliography

[1] V. Barbu and M. Röckner. Nonlinear Fokker-Planck equations with fractional Laplacian and McKean-Vlasov SDEs with L ́evy-Noise. arXiv 2210.05612, PTRF (2024), online

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