Markovian trees subject to catastrophes: would they survive forever?
Date
2013
Authors
Hautphenne, S.
Latouche, G.
Nguyen, G.
Editors
Latouche, G.
Ramaswami, V.
Sethuraman, J.
Sigman, K.
Squillante, M.
Yao, D.
Ramaswami, V.
Sethuraman, J.
Sigman, K.
Squillante, M.
Yao, D.
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Conference paper
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
Statement of Responsibility
Sophie Hautphenne, Guy Latouche, and Giang T. Nguyen
Conference Name
7th International Conference on Matrix- Analytic Methods in Stochastic Models (MAM7 ) (13 Jun 2011 - 16 Jun 2011 : New York)
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.
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© Springer Science+Business Media New York 2013