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This paper studies the rate of convergence to equilibrium for two diffusion models that arise naturally in the queueing context: two-sided reflected Brownian motion and the Ornstein–Uhlenbeck process. Specifically, we develop exact asymptotics and upper bounds on total variation distance to equilibrium, which can be used to assess the quality of the steady state as an approximation to finite-horizon...
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...
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