報告題目：Density of parabolic Anderson random variable
報 告 人：Professor Yaozhong Hu University of Alberta at Edmonton，Canada
報告時間：2020年6月16日 10：00-11：00
報告地點：釘釘會議ID：244 339 7399
校内聯系人：韓月才 hanyc@jlu.edu.cn
報告摘要：
We investigate the shape the density $\rho(t,x; y)$ of the solution $u(t,x)$ to stochastic partial differential equation $\frac{\partial }{\partial t} u(t,x)=\frac12 \Delta u(t,x)+u\diamond \dot W(t,x)$, where $\dot W$ is a general Gaussian noise and $\diamond$ denotes the Wick product. We mainly concern with the asymptotic behavior of $\rho(t,x; y)$ when $y\rightarrow \infty$ or when $t\to0+$. Both upper and lower bounds are obtained and these two bounds match each other modulo some multiplicative constants. If the initial data is positive, then $\rho(t,x;y)$ is supported on the positive half line $y\in [0, \infty)$ and in this case we show that $\rho(t,x; 0+)=0$ and obtain an upper bound for $\rho(t,x; y)$ when $y\rightarrow 0+$.
報告人簡介：
Yaozhong Hu is currently Centennial Professor at University of Alberta at Edmonton. He was elected as a Fellow of Institute of Mathematical Statistics. He now serves as associate editor of Stochastics and Stochastics Report, Acta Mathematica Scientia, and Journal of Applied Mathematics and Stochastic Analysis.
