4th International ICST Workshop on Tools for solving Structured Markov Chains

Research Article

Transient features for Markovian binary trees

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BibTeX Plain Text
  • @INPROCEEDINGS{10.4108/ICST.VALUETOOLS2009.7428,
    author={Sophie Hautphenne and Guy Latouche and Marie-Ange Remiche},
    title={Transient features for Markovian binary trees},
    proceedings={4th International ICST Workshop on Tools for solving Structured Markov Chains},
    publisher={ACM},
    proceedings_a={SMCTOOLS},
    year={2010},
    month={5},
    keywords={Branching processes; matrix analytic methods; transient measures},
    doi={10.4108/ICST.VALUETOOLS2009.7428}
}
  • Sophie Hautphenne
    Guy Latouche
    Marie-Ange Remiche
    Year: 2010
    Transient features for Markovian binary trees
    SMCTOOLS
    ICST
    DOI: 10.4108/ICST.VALUETOOLS2009.7428
Sophie Hautphenne1,*, Guy Latouche1,*, Marie-Ange Remiche1,*
  • 1: Université Libre de Bruxelles Boulevard du Triomphe 1050 Bruxelles, Belgium
*Contact email: shautphe@ulb.ac.be, latouche@ulb.ac.be, mremiche@ulb.ac.be

Abstract

We analyze a particular class of continuous-time multi-type branching processes, namedMarkovian binary trees (MBTs), and we focus on transient measures, such as the distribution of the population size at a fnite time, the distribution of the time until extinction, and the distribution of the to- tal family size until a given time, as well as the total size until extinction. Our results mainly are formulated as dif- ferential equations for probability generating functions and expressions for the factorial moments. They are applied to a demographic comparison of three countries

Keywords
Branching processes; matrix analytic methods; transient measures
Published
2010-05-16
Publisher
ACM
Modified
2010-05-16
http://dx.doi.org/10.4108/ICST.VALUETOOLS2009.7428
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