Journal of Applied Probability

Markov-modulated Brownian motion with two reflecting barriers

Jevgenijs Ivanovs

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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

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

First available in Project Euclid: 4 January 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J55: Local time and additive functionals
Secondary: 60K25: Queueing theory [See also 68M20, 90B22] 60K37: Processes in random environments

Markov additive process fluid model finite buffer two-sided reflection inverse local time overflow process


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

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