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 $y\rightarrow 0+$.
