On the spatial dynamics of the solution to the stochastic heat equation

Sigurd Assing, James Bichard

We consider the solution of ${\partial }_{t}u={\partial }_x^{2}u+{\partial }_x{\partial }_{t}B,(x,t)\in R\times (0,\infty )$, subject to $u(x,0)=0,x\in R$, where $B$ is a Brownian sheet. We sho…