Title: Time reversal and the dynamics of diffusion processes
Speaker: Professor Christian Leonard (Universite Paris Nanterre)
Time: Friday, June 30, 2023, 15:45-16:45
Location: Zoom ID：876 0592 8254, Password：2023
Abstract: During the sixties, Ed Nelson initiated the mathematical investigation of the dynamical properties of the Brownian motion. Two key ingredients of his approach were time reversal and stochastic derivatives, allowing the introduction of the notions of current and osmotic velocities.
ln the same spirit, we present a generalization and an extension of his results under some finite entropy assumption. In particular, the entropic interpolations of a diffusion process between two prescribed marginals are shown to solve some least action principle in the Otto-Wasserstein space (equipped with the Riemannian metric of the quadratic optimal transport). Some well-known consequences in terms of Otto-Wasserstein gradient flows and contraction inequalities are recovered.
Some of these results were obtained in collaboration with P. Cattiaux, G Conforti and I. Gentil.
Biography: Christian Leonard got his PhD at Universit Paris-Sud Orsay in 1984. He became a professor of mathematics at the Unversite Paris Nanterre from 1992 (until now). His research team is Modal'X. He works in probability theory and functional analysis. His favourite keywords are: entropy, optimal transport and large deviations.
More information about HIT-WHU Seminar on Stochastic Analysis and Algorithms can be found here.