Approximations in population-dependent branching processes

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We consider models of population size dependent branching processes with the feature that they are supercritical when population reaches some threshold K, near critical around that value, and subcritical below it. Although such population die out with probability one, their time to extinction is large. We show that this time is exponential in K. Approximations to the populations size in various domains are given, and a problem of small initial population size is discussed. From a technical point of view, analysis of such processes involves techniques of density dependent models as small random perturbations of dynamical systems, and size-dependent bounds.
Original languageEnglish
Title of host publicationLecture Notes in Statistics - Proceedings
EditorsM V Gonzalez, I M del Puerto, R Martinez, M Molina, M Mota, A Ramos
Place of PublicationGermany
PublisherSpringer-Verlag London Ltd.
Pages71 - 78
Number of pages8
ISBN (Print)9783642111549
Publication statusPublished - 2010
EventWorkshop on Branching Processes and their Applications 2009 - Badajoz, Spain
Duration: 20 Apr 200923 Apr 2009
Conference number: 1st (Conference Proceedings)


ConferenceWorkshop on Branching Processes and their Applications 2009
Abbreviated titleWBPA 2009
Internet address

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