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- Sagitov, Serik, 1956, et al.
(författare)
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Extinction times for a birth-death process with weak competition
- 2013
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Ingår i: Lithuanian Mathematical Journal. - : Springer Science and Business Media LLC. - 0363-1672 .- 1573-8825. ; 53:2, s. 220-234
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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