Approximations in population-dependent branching processes

Fima C Klebaner

doi:10.1007/978-3-642-11156-3_5

Approximations in population-dependent branching processes

Fima C Klebaner

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

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 language	English
Title of host publication	Lecture Notes in Statistics - Proceedings
Editors	M V Gonzalez, I M del Puerto, R Martinez, M Molina, M Mota, A Ramos
Place of Publication	Germany
Publisher	Springer-Verlag London Ltd.
Pages	71 - 78
Number of pages	8
Volume	197
ISBN (Print)	9783642111549
DOIs	https://doi.org/10.1007/978-3-642-11156-3_5
Publication status	Published - 2010
Event	Workshop on Branching Processes and their Applications 2009 - Badajoz, Spain Duration: 20 Apr 2009 → 23 Apr 2009 Conference number: 1st http://www.springer.com/us/book/9783642111549 (Conference Proceedings)

Conference

Conference	Workshop on Branching Processes and their Applications 2009
Abbreviated title	WBPA 2009
Country/Territory	Spain
City	Badajoz
Period	20/04/09 → 23/04/09
Internet address	http://www.springer.com/us/book/9783642111549 (Conference Proceedings)

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10.1007/978-3-642-11156-3_5

Cite this

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title = "Approximations in population-dependent branching processes",

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.",

author = "Klebaner, {Fima C}",

year = "2010",

doi = "10.1007/978-3-642-11156-3_5",

language = "English",

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volume = "197",

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editor = "Gonzalez, {M V} and {del Puerto}, {I M} and R Martinez and M Molina and M Mota and A Ramos",

booktitle = "Lecture Notes in Statistics - Proceedings",

publisher = "Springer-Verlag London Ltd.",

address = "Germany",

note = "Workshop on Branching Processes and their Applications 2009, WBPA 2009 ; Conference date: 20-04-2009 Through 23-04-2009",

url = "http://www.springer.com/us/book/9783642111549",

}

Klebaner, FC 2010, Approximations in population-dependent branching processes. in MV Gonzalez, IM del Puerto, R Martinez, M Molina, M Mota & A Ramos (eds), Lecture Notes in Statistics - Proceedings. vol. 197, Springer-Verlag London Ltd., Germany, pp. 71 - 78, Workshop on Branching Processes and their Applications 2009, Badajoz, Spain, 20/04/09. https://doi.org/10.1007/978-3-642-11156-3_5

Approximations in population-dependent branching processes. / Klebaner, Fima C.
Lecture Notes in Statistics - Proceedings. ed. / M V Gonzalez; I M del Puerto; R Martinez; M Molina; M Mota; A Ramos. Vol. 197 Germany: Springer-Verlag London Ltd., 2010. p. 71 - 78.

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

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N1 - Conference code: 1st

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N2 - 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.

AB - 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.

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DO - 10.1007/978-3-642-11156-3_5

M3 - Conference Paper

SN - 9783642111549

VL - 197

SP - 71

EP - 78

BT - Lecture Notes in Statistics - Proceedings

A2 - Gonzalez, M V

A2 - del Puerto, I M

A2 - Martinez, R

A2 - Molina, M

A2 - Mota, M

A2 - Ramos, A

PB - Springer-Verlag London Ltd.

CY - Germany

T2 - Workshop on Branching Processes and their Applications 2009

Y2 - 20 April 2009 through 23 April 2009

ER -

Approximations in population-dependent branching processes

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