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Type: Conference paper
Title: Markovian trees subject to catastrophes: would they survive forever?
Author: Hautphenne, S.
Latouche, G.
Nguyen, G.
Citation: Springer Proceedings in Mathematics and Statistics, 2013 / Latouche, G., Ramaswami, V., Sethuraman, J., Sigman, K., Squillante, M., Yao, D. (ed./s), vol.27, pp.87-106
Publisher: Springer Science & Business Media
Issue Date: 2013
Series/Report no.: Springer Proceedings in Mathematics & Statistics; 27
ISBN: 146144909X
ISSN: 2194-1009
Conference Name: 7th International Conference on Matrix- Analytic Methods in Stochastic Models (MAM7 ) (13 Jun 2011 - 16 Jun 2011 : New York)
Editor: Latouche, G.
Ramaswami, V.
Sethuraman, J.
Sigman, K.
Squillante, M.
Yao, D.
Statement of
Sophie Hautphenne, Guy Latouche, and Giang T. Nguyen
Abstract: We consider multitype Markovian branching processes subject to catastrophes which kill random numbers of living individuals at random epochs. It is well known that the criteria for the extinction of such a process is related to the conditional growth rate of the population, given the history of the process of catastrophes, and that it is usually hard to evaluate. We give a simple characterization in the case where all individuals have the same probability of surviving a catastrophe, and we determine upper and lower bounds in the case where survival depends on the type of individual. The upper bound appears to be often much tighter than the lower bound.
Keywords: Branching processes; matrix-analytic methods; catastrophes; extinction criteria; Lyapunov exponent
Rights: © Springer Science+Business Media New York 2013
DOI: 10.1007/978-1-4614-4909-6_5
Appears in Collections:Aurora harvest 7
Mathematical Sciences publications

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