Weak convergence of reflecting Brownian motions
It is not easy to get a reflected Brownian motion on the closure of an arbitrary bounded open domain \(D\). This note gives a simple proof of the following facts: If \(D_k\) is an increasing sequence of domains with continuous boundaries and with limit \(D\), then the reflected Brownian motion on \(\overline D\) is the weak limit of the reflected Brownian motions on \(\overline D_k\). The paper ends with a discussion on the known results about the construction of reflected Brownian motions on more general domains.
scientific article; zbMATH DE number 1171022