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- Title
On the rate of convergence to equilibrium for reflected Brownian motion.
- Authors
Glynn, Peter W.; Wang, Rob J.
- Abstract
This paper discusses the rate of convergence to equilibrium for one-dimensional reflected Brownian motion with negative drift and lower reflecting boundary at 0. In contrast to prior work on this problem, we focus on studying the rate of convergence for the entire distribution through the total variation norm, rather than just moments of the distribution. In addition, we obtain computable bounds on the total variation distance to equilibrium that can be used to assess the quality of the steady state for queues as an approximation to finite horizon expectations.
- Subjects
STOCHASTIC convergence; BROWNIAN motion; EQUILIBRIUM; APPROXIMATION theory; MATHEMATICAL bounds; STEADY state conduction
- Publication
Queueing Systems, 2018, Vol 89, Issue 1/2, p165
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-018-9574-1