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arXiv · 1508.00922

Slowing time: Markov-modulated Brownian motion with a sticky boundary

Guy Latouche·Giang T. Nguyen
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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.

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Guy Latouche, Giang T. Nguyen. 2015-08-04. Slowing time: Markov-modulated Brownian motion with a sticky boundary. https://arxiv.org/abs/1508.00922

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