MARKOVIAN TREES SUBJECT TO CATASTROPHES: TRANSIENT FEATURES AND EXTINCTION PROBABILITY
Sophie Hautphenne, Guy Latouche
STOCHASTIC MODELS | TAYLOR & FRANCIS INC | Published : 2011
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.
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Awarded by Australian Research Council
This work has been conducted when the first author was an Aspirant of the Fonds National de la Recherche Scientifique (F.R.S. - F.N.R.S.). The authors also acknowledge the support from the ARC grant AUWB-08/13-ULB 5 financed by the Ministere de la Communaute francaise de Belgique, and the support of the Australian Research Council, grant Nb. DP110101663.