一、报告题目

Necessary and sufficient conditions to solve parabolic Anderson model with rough noise

二、主讲人

王雄

三、报告时间

2022年7月6日9:30-11:30

四、报告地点

腾讯会议ID:713 635 577

五、摘要

We obtain necessary and sufficient conditions for the existence of $n$-th chaos of the solution to the parabolic Anderson model $\frac{\partial}{\partial t}u(t,x)=\frac{1}{2}\Delta u(t,x)+u(t,x)\dot{W}(t,x)$, where $\dot{W}(t,x)$ is a fractional Brownian field with temporal Hurst parameter $H_0\ge 1/2$ and spatial parameters $H$ $ =(H_1, \cdots, H_d)$ $ \in (0, 1)^d$.

When $d=1$, we extend the condition on the parameters under which the chaos expansion of the solution is convergent in the mean square sense, which is both sufficient and necessary under some circumstances.

六、主讲人简介

Xiong Wang otained his PhD degree at University of Alberta in June 2022. His current research focuses on stochastic partial differential equations (SPDEs) and stochastic differential equations (SDEs).

七、主办单位

非线性期望前沿科学中心

数学与交叉科学研究中心