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Algorithmic Approach to the Extinction Probability of Branching Processes

Author

Listed:
  • Sophie Hautphenne

    (Université Libre de Bruxelles)

  • Guy Latouche

    (Université Libre de Bruxelles)

  • Marie-Ange Remiche

    (Université Libre de Bruxelles)

Abstract

The extinction probability of a branching process is characterized as the solution of a fixed-point equation which, for a fairly general class of Markovian branching processes, is vector quadratic. We address the question of solving that equation, using a mixture of algorithmic and probabilistic arguments. We compare the relative efficiency of three iterative methods based on functional iteration, on the basis of the probabilistic interpretation of the successive iterations as well as on the basis of traditional rate of convergence analysis. We illustrate our findings through a few numerical examples and conclude by showing how they extend to more complex systems.

Suggested Citation

  • Sophie Hautphenne & Guy Latouche & Marie-Ange Remiche, 2011. "Algorithmic Approach to the Extinction Probability of Branching Processes," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 171-192, March.
    • Handle: RePEc:spr:metcap:v:13:y:2011:i:1:d:10.1007_s11009-009-9141-7
    DOI: 10.1007/s11009-009-9141-7
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    References listed on IDEAS

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    1. Nigel Bean & Nectarios Kontoleon & Peter Taylor, 2008. "Markovian trees: properties and algorithms," Annals of Operations Research, Springer, vol. 160(1), pages 31-50, April.
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    Cited by:

    1. Hautphenne, Sophie & Massaro, Melanie & Turner, Katharine, 2019. "Fitting Markovian binary trees using global and individual demographic data," Theoretical Population Biology, Elsevier, vol. 128(C), pages 39-50.

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