Exponential ergodicity and convergence for generalized reflected Brownian motion

TL;DR

This paper proves exponential ergodicity for a class of multidimensional reflected Brownian motions, including the O'Connell-Yor process, by establishing an exponential drift condition, and discusses related open problems.

Contribution

It introduces a new convergence analysis for Brownian queues in tandem, demonstrating uniform exponential ergodicity for these processes.

Findings

Established exponential ergodicity for generalized reflected Brownian motion

Proved uniform exponential convergence for the O'Connell-Yor process

Presented open problems in the area

Abstract

In this paper we provide convergence analysis for a class of Brownian queues in tandem by establishing an exponential drift condition. A consequence is the uniform exponential ergodicity for these multidimensional diffusions, including the O'Connell-Yor process. A list of open problems are also presented.