Markov modulation of a two-sided reflected Brownian motion with application to fluid queues

D’Auria, Bernardo and Offer Kella

Stochastic Processes and their Applications, 2012, vol. 122, issue 4, 1566-1581

Abstract: In this paper, we study a reflected Markov-modulated Brownian motion with a two sided reflection in which the drift, diffusion coefficient and the two boundaries are (jointly) modulated by a finite state space irreducible continuous time Markov chain. The goal is to compute the stationary distribution of this Markov process, which in addition to the complication of having a stochastic boundary can also include jumps at state change epochs of the underlying Markov chain because of the boundary changes. We give the general theory and then specialize to the case where the underlying Markov chain has two states.

Keywords: Markov modulation; Brownian motion; Two sided reflection; Fluid queues (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:122:y:2012:i:4:p:1566-1581

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DOI: 10.1016/j.spa.2012.02.001

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