Long time asymptotics for constrained diffusions in polyhedral domains

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:117

Article

Budhiraja, Amarjit ; Lee, Chihoon

关键词: sernimartingale reflecting Brownian motion;    phi-irreducibility;    V-uniform ergodicity;    geometric ergodicity;    constrained diffusions;    heavy traffic;    Poisson equation;    moment stability;    functional central limit theorems;   

DOI  :  10.1016/j.spa.2006.11.007

来源: Elsevier

【 摘 要 】

We study long time asymptotic properties of constrained diffusions that arise in the heavy traffic analysis of multiclass queueing networks. We first consider the classical diffusion model with constant coefficients, namely a semimartingale reflecting Brownian motion (SRBM) in a d-dimensional positive orthant. Under a natural stability condition on a related deterministic dynamical system [P. Dupuis, R.J. Williams, Lyapunov functions for semimartingale reflecting brownian motions, Annals of Probability 22 (2) (1994) 680-702] showed that an SRBM is ergodic. We strengthen this result by establishing geometric ergodicity for the process. As consequences of geometric ergodicity we obtain finiteness of the moment generating function of the invariant measure in a neighborhood of zero, uniform time estimates for polynomial moments of all orders, and functional central limit results. Similar long time properties are obtained for a broad family of constrained diffusion models with state dependent coefficients under a natural condition on the drift vector field. Such models arise from heavy traffic analysis of queueing networks with state dependent arrival and service rates. (c) 2006 Elsevier B.V. All rights reserved.

【 授权许可】

Free