Reflected Diffusions, Dirichlet Processes and Heavy-traffic limits

ABSTRACT

Dirichlet processes are a generalization of semimartingales, which have many useful properties that make them amenable to computation. We show that a large class of reflected diffusions can be characterized as Dirichlet processes.  As an illustration of how these processes arise naturally in applications, we provide concrete examples of stochastic networks whose heavy traffic limits are not semimartingales but are nevertheless Dirichlet processes.  We also provide a characterization of the stationary distribution of these processes.