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Markov-Modulated Brownian Motion with Temporary Change of Regime at Level Zero

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Listed:
  • Guy Latouche

    (Université libre de Bruxelles (ULB))

  • Matthieu Simon

    (Université libre de Bruxelles (ULB))

Abstract

We determine the stationary distribution of a one-sided Markov-Modulated Brownian Motion (MMBM) of which the behaviour is modified during the intervals between a visit to level zero and the next visit to a fixed positive level b. We use the semi-regenerative structure of the process, and we also use the fluid approximation for MMBMs introduced by Latouche and Nguyen in 2015. Finally, we show how the expressions can be simplified in some interesting special cases and we conclude by providing some numerical illustrations.

Suggested Citation

  • Guy Latouche & Matthieu Simon, 2018. "Markov-Modulated Brownian Motion with Temporary Change of Regime at Level Zero," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1199-1222, December.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:4:d:10.1007_s11009-017-9602-3
    DOI: 10.1007/s11009-017-9602-3
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    References listed on IDEAS

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    1. D’Auria, Bernardo & Kella, Offer, 2012. "Markov modulation of a two-sided reflected Brownian motion with application to fluid queues," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1566-1581.
    2. Rajeeva L. Karandikar & Vidyadhar G. Kulkarni, 1995. "Second-Order Fluid Flow Models: Reflected Brownian Motion in a Random Environment," Operations Research, INFORMS, vol. 43(1), pages 77-88, February.
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    Cited by:

    1. Nguyen, Giang T. & Peralta, Oscar, 2020. "An explicit solution to the Skorokhod embedding problem for double exponential increments," Statistics & Probability Letters, Elsevier, vol. 165(C).

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