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

Guy Latouche () and Matthieu Simon ()
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Guy Latouche: Université libre de Bruxelles (ULB)
Matthieu Simon: Université libre de Bruxelles (ULB)

Methodology and Computing in Applied Probability, 2018, vol. 20, issue 4, 1199-1222

Abstract: 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.

Keywords: Stochastic processes; Markov-modulated Brownian motion; Stationary distribution; Matrix analytic methods; Semi-regenerative processes; 60J65; 66K37; 60J25; 60K15 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-017-9602-3

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