Markov-modulated Brownian motion with two reflecting barriers

Details Markov-modulated Brownian motion with two reflecting barriers Markov-modulated Brownian motion with two reflecting barriers

2010-03-22

arxiv.org/abs/1003.4107v2

Mathematics

Probability

13 pages, 1 figure

Scientific paper

We consider a Markov-modulated Brownian motion reflected to stay in a strip [0,B]. The stationary distribution of this process is known to have a simple form under some assumptions. We provide a short probabilistic argument leading to this result and explaining its simplicity. Moreover, this argument allows for generalizations including the distribution of the reflected process at an independent exponentially distributed epoch. Our second contribution concerns transient behavior of the reflected system. We identify the joint law of the processes t,X(t),J(t) at inverse local times.

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