A random string with reflection in a convex domain

Abstract

We study the motion of a random string in a convex domain $O$ in ${\mathbb{R}}^d$, namely the solution of a vector-valued stochastic heat equation, confined in the closure of $O$ and reflected at the boundary of $O$. We study the structure of the reflection measure by computing its Revuz measure in terms of an infinite-dimensional integration by parts formula. Our method exploits recent results on weak convergence of Markov processes with log-concave invariant measures.