Approximations in population-dependent branching processes

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Abstract

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
Volume197
ISBN (Print)9783642111549
DOIs
Publication statusPublished - 2010
EventWorkshop on Branching Processes and their Applications 2009 - Badajoz, Spain
Duration: 20 Apr 200923 Apr 2009
Conference number: 1st
http://www.springer.com/us/book/9783642111549 (Conference Proceedings)

Conference

ConferenceWorkshop on Branching Processes and their Applications 2009
Abbreviated titleWBPA 2009
CountrySpain
CityBadajoz
Period20/04/0923/04/09
Internet address

Cite this

Klebaner, F. C. (2010). Approximations in population-dependent branching processes. In M. V. Gonzalez, I. M. del Puerto, R. Martinez, M. Molina, M. Mota, & A. Ramos (Eds.), Lecture Notes in Statistics - Proceedings (Vol. 197, pp. 71 - 78). Springer-Verlag London Ltd.. https://doi.org/10.1007/978-3-642-11156-3_5