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

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• 作者：Bernardo D&rsquo ; Auria^a ; ^{bernardo.dauria@uc3m.es} ; ; Offer Kella^b ; ^{Offer.Kella@huji.ac.il} ;
• 关键词：Markov modulation ; Brownian motion ; Two sided reflection ; Fluid queues
• 刊名：Stochastic Processes and their Applications
• 出版年：2012
• 期刊代码：57_03044149
• 类别：mt
• 出版时间：April, 2012
• 卷：122
• 期：4
• 页码：1566-1581
• 文件大小：244 K

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.