A Random String with Reflection in a Convex Domain
Said Karim Bounebache · Stochastic Analysis and Applications · 2011
We study the motion of a random string in a convex domain O in 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.