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Speaker:Wang Xiong, Dctor, University of Alberta
Date:July. 6, 2022
Time:9:30-11:30
Location:Tencent Meeting,ID:713 635 577
Sponsor:Research Center for Mathematics and Interdisciplinary Sciences
Research Center for Nonlinear Expectation
Abstract:
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.
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https://www.view.sdu.edu.cn/info/1020/167321.htm