Probability Seminars——Stochastic heat equations taking values in a Riemannian manifold
主 题: Probability Seminars——Stochastic heat equations taking values in a Riemannian manifold
报告人: Xiangchan Zhu (Beijing Jiaotong University)
时 间: 2017-12-11 15:00-16:00
地 点: Room 1418, Sciences Building No. 1
Abstract: In this talk, I talk about the existence of martingale solutions to the stochastic heat equation in a Riemannian manifold by using suitable Dirichlet form on the Riemannian path and loop space. Finally, by using Anderson-Driver's Approximation, we give a form of the equation associated with the process given by Dirichlet form. Moreover, we establish the Log-Sobolev inequality for the stochastic heatequation. In addition, some characterizations for the lower or pinned bounds ofthe Ricci curvature are presented related to the stochastic heat equation.