On the rate of convergence to equilibrium for reflected Brownian motion

@article{Glynn2018OnTR,
  title={On the rate of convergence to equilibrium for reflected Brownian motion},
  author={Peter W. Glynn and Rob J. Wang},
  journal={Queueing Syst.},
  year={2018},
  volume={89},
  pages={165-197}
}
This paper discusses the rate of convergence to equilibrium for onedimensional 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… CONTINUE READING

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