Transient features for Markovian binary trees

Sophie Hautphenne; Guy Latouche; Marie-Ange Remiche

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

Research Article

Transient features for Markovian binary trees

Cite: 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