On the Feynman-Kac Formula

In this article, given $y :[0,\eta)\rightarrow H$ a continuous map into a Hilbert space $H$ we study the equation $$\hat y(t) = e^{\int_0^tc(s,\hat y)}y(t)$$ where $c(s,\cdot)$ is a given `potential' on $C([0,\eta),H)$. Applying the transformation $y \rightarrow \hat y$ to the solutions of the SPDE and PDE underlying a diffusion, we study the Feynman-Kac formula.