Reduced subcritical Galton-Watson processes in a random environment

We study the structure of genealogical trees of reduced subcritical Galton-Watson processes in a random environment assuming that all (randomly varying in time) offspring generating functions are fractional linear. We show that this structure may differ significantly from that of the ‘classical’ red...

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Bibliographic Details
Published in:Advances in applied probability 1999-03, Vol.31 (1), p.88-111
Main Authors: Fleischmann, Klaus, Vatutin, Vladimir A.
Format: Article
Language:English
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Summary:We study the structure of genealogical trees of reduced subcritical Galton-Watson processes in a random environment assuming that all (randomly varying in time) offspring generating functions are fractional linear. We show that this structure may differ significantly from that of the ‘classical’ reduced subcritical Galton-Watson processes. In particular, it may look like a complex ‘hybrid’ of classical reduced super and subcritical processes. Some relations with random walks in a random environment are discussed.
ISSN:0001-8678
1475-6064
DOI:10.1017/S0001867800008971