The Semimartingale Structure of Reflecting Brownian Motion

We prove that reflecting Brownian motion on a bounded Lipschitz domain is a semimartingale. We also extend the well-known Skorokhod equation to this case. In this note we study the semimartingale property and the Skorokhod equation of reflecting Brownian motion on a bounded Euclidean domain. A R d_ valued continuous stochastic process X = {Xt ; t > 0} is said to be a semimartingale if it can be decomposed into the form