Markov-modulated Brownian motions perturbed by catastrophes. Issue 2 (17th February 2020)

• Record Type: Journal Article
• Authors: Simon, Matthieu
• Is Part Of: Stochastics. Volume 92:Issue 2(2020)
• Page Start: 275
• Page End: 296
• Publication Date: 2020-02-17
• Subjects: Markov-modulated Brownian motion -- catastrophes -- stationary distribution -- semi-regenerative processes -- matrix analytic methods; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2019.1624753
• Languages: English
• ISSNs: 1744-2508

Abstract

ABSTRACT: We consider a one-sided Markov-modulated Brownian motion perturbed by catastrophes that occur at some rates depending on the modulating process. When a catastrophe occurs, the level drops to zero for a random recovery period. Then the process evolves normally until the next catastrophe. We use a semi-regenerative approach to obtain the stationary distribution of this perturbed MMBM. Next, we determine the stationary distribution of two extensions: we consider the case of a temporary change of regime after each recovery period and the case where the catastrophes can only happen above a fixed threshold. We provide some simple numerical illustrations.