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Markovian trees subject to catastrophes: Transient features and extinction probability

par Hautphenne, Sophie ;Latouche, Guy
Référence Stochastic models, 27, 4, page (569-590)
Publication Publié, 2011

Article révisé par les pairs

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Résumé :

We study transient features and the extinction probability of a particular class of multitype Markovian branching processes called Markovian binary trees, subject at random epochs to catastrophes, controlled by a Markovian arrival process, and killing random numbers of living individuals. We provide two types of probabilistic methods to numerically compute the extinction probability: the first one is based on an integral equation for the probability generating function of the population size, and the second one is based on the correspondence between Markovian branching processes with catastrophes and structured Markov chains of G/M/1-type. © Taylor & Francis Group, LLC.