Random dynamical systems of SPDE driven by a fractional Brownian motion
主 题: Random dynamical systems of SPDE driven by a fractional Brownian motion
报告人: Prof. Bjoern Schmalfuss (Friedrich-Schiller-Universität Jena)
时 间: 2016-07-20 15:30-16：30
地 点: 理科一号楼1365室
We consider the SPDE \[du=(Au+F(u))dt+G(u)dB^H, \quad u(0)\in V \], where $V$ is a separable Hilbert space and $B^H$ is a fractional Brownian motion with Hurst parameter in $(1/2,1)$. The coefficients $F$ and $G$ are sufficiently smooth. We show that this equation has a unique solution which generates a random dynamical system. We discuss the longtime behavior of this random dynamical system. We also give a remark for the case that the Hurst parameter is in (1/3,1/2].