时 间：2023年11月7日 10:00-11:30
地 点: 腾讯会议ID： 560-4756-7741
报告人：Yaozhong Hu 阿尔伯塔大学教授
主持人：徐方军 华东师范大学教授
摘 要：
Let $u(t,x)$ be the solution to a stochastic partial differential equation $\frac{\partial }{\partial t} u(t,x)=\frac{1}{2}\Delta u(t,x)+u\diamond \dot W(t,x)$, where $\dot W$ is a general Gaussian noise and $\diamond$ denotes the Wick product. For fixed $(t,x)\in \R_+\times \R^d$, we shall discuss the existence and the shape of the density $\rho(t,x; y)$ (as a function of $y$) of the random variable $u(t,x)$. We mainly concern with the asymptotic behavior of $\rho(t,x; y)$ when $y\rightarrow \infty$ or when $t\to 0+$. Both upper and lower bounds are obtained and these two bounds match each other modulo some multiplicative constants. If the initial condition 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 $y\rightarrow 0+$.
报告人简介：
Yaozhong Hu，加拿大阿尔伯塔大学Centennial Professor。1992年获法国路易斯巴斯德大学概率博士学位，师从著名概率学家P. A. Meyer教授。2015年当选Fellow of Institute of Mathematical Statistics。主要从事随机分析和随机控制的研究。在Ann. Probability、Probab.Theory Related Fields、Ann. Applied Probability、 Bernoulli、Stochatis Process. Appl.、Mem. Amer. Math. Soc.、Comm. PDEs、J. Funct. Anal、Trans. Amer. Math. Soc等期刊上发表论文170多篇，出版专著2部。