Slowing time: Markov-modulated Brownian motion with a sticky boundary
Probability
2015-08-06 v1
Abstract
We analyze the stationary distribution of regulated Markov modulated Brownian motions (MMBM) modified so that their evolution is slowed down when the process reaches level zero --- level zero is said to be {\em sticky}. To determine the stationary distribution, we extend to MMBMs a construction of Brownian motion with sticky boundary, and we follow a Markov-regenerative approach similar to the one developed in past years in the context of quasi-birth-and-death processes and fluid queues. We also rely on recent work showing that Markov-modulated Brownian motions may be analyzed as limits of a parametrized family of fluid queues. We use our results to revisit the stationary distribution of the well-known regulated MMBM.
Keywords
Cite
@article{arxiv.1508.00922,
title = {Slowing time: Markov-modulated Brownian motion with a sticky boundary},
author = {Guy Latouche and Giang T. Nguyen},
journal= {arXiv preprint arXiv:1508.00922},
year = {2015}
}