On the Feynman-Kac Formula

Abstract

In this article, given $y:[0,\eta )\to H$ 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 $y\to \hat{y}$ to the solutions of the SPDE and PDE underlying a diffusion, we study the Feynman-Kac formula.