A Feynman-Kac approach for the spatial derivative of the solution to the Wick stochastic heat equation driven by time homogeneous white noise

Hyun-Jung Kim, Ramiro Scorolli

We consider the (unique) mild solution $u(t,x)$ of a 1-dimensional stochastic heat equation on $[0,T]\times \mathbb{R}$ driven by time-homogeneous white noise in the Wick-Skorokhod s…