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

Bernardo D'Auria, Offer Kella

Research output: Contribution to journalArticlepeer-review

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.

Original languageAmerican English
Pages (from-to)1566-1581
Number of pages16
JournalStochastic Processes and their Applications
Volume122
Issue number4
DOIs
StatePublished - Apr 2012

Keywords

  • Brownian motion
  • Fluid queues
  • Markov modulation
  • Two sided reflection

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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