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Markovian Trees Subject to Catastrophes: Would They Survive Forever?

  • Sophie HautphenneEmail author
  • Guy Latouche
  • Giang T. Nguyen
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 27)

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.

Key words

branching processes matrix-analytic methods catastrophes extinction criteria Lyapunov exponent 

Notes

Acknowledgements

This work was subsidized by the ARC Grant AUWB-08/13–ULB 5 financed by the Ministère de la Communauté française de Belgique. The first author also gratefully acknowledges the support from the Fonds de la Recherche Scientifique (FRS-FNRS) and from the Australian Research Council, Grant No. DP110101663.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Sophie Hautphenne
    • 1
    Email author
  • Guy Latouche
    • 2
  • Giang T. Nguyen
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of MelbourneVictoriaAustralia
  2. 2.Département d’informatiqueUniversité libre de BruxellesBrusselsBelgium

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