Extinction times for a birth-death process with weak competition
نویسندگان
چکیده
We consider a birth-death process with the birth rates iλ and death rates iμ+i(i−1)θ, where i is the current state of the process. A positive competition rate θ is assumed to be small. In the supercritical case when λ > μ this process can be viewed as a demographic model for a population with a high carrying capacity around λ−μ θ . The article reports in a self-contained manner on the asymptotic properties of the time to extinction for this logistic branching process as θ → 0. All three reproduction regimes λ > μ, λ < μ, and λ = μ are studied. Mathematics Subject Classification: 60J80
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تاریخ انتشار 2012