题目：Time reversal and the dynamics of diffusion processes
报告人：Christian Leonard 教授 (巴黎第十大学)
时间：6月30日（星期五），15:45-16:45
地点：Zoom会议，会议号：876 0592 8254，密码：2023
摘要：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.
报告人简介：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.
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