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

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  • D’Auria, Bernardo
  • Kella, Offer
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 122 (2012)
    Issue (Month): 4 ()
    Pages: 1566-1581

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    Handle: RePEc:eee:spapps:v:122:y:2012:i:4:p:1566-1581

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    Related research

    Keywords: Markov modulation; Brownian motion; Two sided reflection; Fluid queues;

    References

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    1. Z. Jiang & M. R. Pistorius, 2008. "On perpetual American put valuation and first-passage in a regime-switching model with jumps," Papers 0803.2302, arXiv.org.
    2. Zhengjun Jiang & Martijn Pistorius, 2008. "On perpetual American put valuation and first-passage in a regime-switching model with jumps," Finance and Stochastics, Springer, vol. 12(3), pages 331-355, July.
    3. Sotomayor, Luz R. & Cadenillas, Abel, 2011. "Classical and singular stochastic control for the optimal dividend policy when there is regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 344-354, May.
    4. Bernardo D'Auria & Offer Kella, & Jevgenijs Ivanovs & Michel Mandjes, 2010. "First passage of a Markov additive process and generalized Jordan chains," Statistics and Econometrics Working Papers ws103923, Universidad Carlos III, Departamento de Estadística y Econometría.
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