A Structured Markov Chain Approach to Branching Processes

Sophie Hautphenne

Journal article

A Structured Markov Chain Approach to Branching Processes

Sophie Hautphenne

STOCHASTIC MODELS | TAYLOR & FRANCIS INC | Published : 2015

DOI: 10.1080/15326349.2015.1022264

Abstract

Algorithmic methods developed for structured Markov chains are extended to solve questions about a class of continuous-time branching processes called Markovian binary trees (MBTs). This approach allows us to compute the extinction probability of an MBT, the distribution of its maximal size given extinction, the expected time until extinction, and the mean time until the tree reaches a given size. The resulting algorithms are efficient in practice for processes of relatively small dimension. The numerical methods are illustrated on MBTs evolving in a Markovian random environment.

University of Melbourne Researchers

Sophie Hautphenne Author Mathematics and Statistics

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Grants

Awarded by ARC - Ministere de la Communaute francaise de Belgique

Awarded by Australian Research Council

Funding Acknowledgements

The author also acknowledges the support from the ARC grant AUWB-08/13-ULB 5 financed by the Ministere de la Communaute francaise de Belgique, and the support of the Australian Research Council, grants No. DP110101663 and FL130100039.