A boundary property of semimartingale reflecting Brownian motions.

We consider a class of reflecting Brownian motions on the non- negative orthant in R sup K. In the interior of the orthant, such a process behaves like Brownian motion with a constant covariance matrix and drift vector. At each of the (K-1)-dimensional faces that form the boundary of the orthant, the process reflects instantaneously in a direction that is constant over the face. We give necessary condition for the process to have a certain semimartingale decomposition, and then show that the boundary processes appearing in this decomposition do not charge the set of times that the process is at the intersection of two or more faces.