## Journal of Applied Probability

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

Jevgenijs Ivanovs

#### Abstract

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 explain 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 model. We identify the joint law of the processes defining the model at inverse local times.

#### Article information

Source
J. Appl. Probab. Volume 47, Number 4 (2010), 1034-1047.

Dates
First available in Project Euclid: 4 January 2011

http://projecteuclid.org/euclid.jap/1294170517

Digital Object Identifier
doi:10.1239/jap/1294170517

Mathematical Reviews number (MathSciNet)
MR2752892

Zentralblatt MATH identifier
1213.60127

#### Citation

Ivanovs, Jevgenijs. Markov-modulated Brownian motion with two reflecting barriers. J. Appl. Probab. 47 (2010), no. 4, 1034--1047. doi:10.1239/jap/1294170517. http://projecteuclid.org/euclid.jap/1294170517.

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