Special Session 16: 

Stochastic heat equation with values in a Riemannian manifold: non-compact case

xiangchan zhu
Beijing Jiaotong University
Peoples Rep of China
Co-Author(s):    
Abstract:
In this talk, we will give the existence of martingale solutions to the stochastic heat equation with spatial variable on the whole line and taking values in a non-compact Riemannian manifold, which admits Wiener measure as an invariant measure by using Dirichlet form. Moreover, we establish the log-Sobolev inequality when Ricci curvature is strictly positive which implies exponential ergodicity for the process. Also when the sectional curvature is negative, the process is non-ergodic.