TITLE: On the stationary measure of a reflected Brownian motion in a wedge: some explicit results

SPEAKER: Dr. Ton Dieker

ABSTRACT:

Multi-dimensional reflected Brownian motion is a Markov process which plays an important role in applications. It is particularly widely used to approximate the behavior of heavily loaded queueing networks. Of special interest is the long-term behavior of the process, i.e., its stationary distribution.

Although the stationary distribution of one-dimensional reflected Brownian motion with drift is exponential, in a multidimensional setting this is only true under a so-called skew symmetry condition on the reflection directions.

Not much is known on the stationary measure (or its density) when the skew symmetry condition fails to hold. For special multidimensional reflected Brownian motions, an intriguingly simple formula arises from connections with the reflection principle. In this formula, the stationary density is represented as a finite sum of exponential terms.

This talk reports an attempt to marry this formula with the literature on two-dimensional reflected Brownian motion in a wedge.

Joint work with J. Moriarty, University of Manchester, UK.