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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

D'Auria, Bernardo¹  Kella, Offer² 

[1] Univ Carlos III Madrid, Madrid 28911, Spain

[2] Hebrew Univ Jerusalem, Dept Stat, IL-91905 Jerusalem, Israel

关键词: Markov modulation;    Brownian motion;    Two sided reflection;    Fluid queues;   

DOI  :  10.1016/j.spa.2012.02.001

来源: Elsevier

【 摘 要 】

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. (c) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free