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

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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.

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Acknowledgements

We thank the referee for a careful analysis and a detailed report. The research of M. Simon was supported by the Belgian F.R.S.-FNRS through an FRIA research grant. We acknowledge the support of the Australian Research Council Center of Excellence for Mathematical and Statistical Frontiers (ACEMS).

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Authors and Affiliations

  1. Faculté des Sciences, Département de Mathématique, Université libre de Bruxelles (ULB), Campus de la Plaine C.P. 210, 1050, Bruxelles, Belgium

    Guy Latouche & Matthieu Simon

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  1. Guy Latouche
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  2. Matthieu Simon
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Correspondence to Matthieu Simon.

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Latouche, G., Simon, M. Markov-Modulated Brownian Motion with Temporary Change of Regime at Level Zero. Methodol Comput Appl Probab 20, 1199–1222 (2018). https://doi.org/10.1007/s11009-017-9602-3

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  • DOI: https://doi.org/10.1007/s11009-017-9602-3

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