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Extinction times for a birth-death process with weak competition

Serik Sagitov (Institutionen för matematiska vetenskaper, matematisk statistik) ; A. Shaimerdenova
Lithuanian Mathematical Journal (0363-1672). Vol. 53 (2013), 2, p. 220-234.
[Artikel, refereegranskad vetenskaplig]

We consider a birth-death process with birth rates i lambda and death rates i mu+i(i-1)theta, where i is the current state of the process. A positive competition rate theta is assumed to be small. In the supercritical case where lambda > mu, this process can be viewed as a demographic model for a population with high carrying capacity around (lambda-mu)/theta. The article reports in a self-contained manner on the asymptotic properties of the time to extinction for this logistic branching process as theta -> 0. All three reproduction regimes lambda > mu, lambda < mu, and lambda = mu are studied.

Nyckelord: birth-death process, carrying capacity, time to extinction, coupling method, logistic branching process

Denna post skapades 2013-07-12. Senast ändrad 2017-09-14.
CPL Pubid: 180127


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Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)



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Denna publikation är ett resultat av följande projekt:

Stochastic models of gene and species trees (VR//2010-5623)