王者体育

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科学研究
报告题目:

density of parabolic anderson random variable

报告人:

huyaozhong jiaoshou(alberta university,canada)

报告时间:

报告地点:

lixueyuandongbeilouerloubaogaoting(209)

报告摘要:

王者体育i will present some results on  the shape estimates of the density $\rho(t,x; y)$ of the solution $u(t,x)$ to 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.  i 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 data is positive, then $\rho(t,x;y)$ is supported on the positive half line $y\in [0, \infty)$  and in this case $\rho(t,x; 0+)=0$   and i will give  n an upper bound for $\rho(t,x; y)$ when $y\rightarrow 0+$.


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