A random string with reflection in a convex domain

Details A random string with reflection in a convex domain A random string with reflection in a convex domain

2010-04-07

arxiv.org/abs/1004.1197v2

Mathematics

Probability

Scientific paper

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.

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