Abstract
We consider a birth–death process with 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 where λ > μ, this process can be viewed as a demographic model for a population with 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.
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1The author was supported by the Swedish Research Council, grant 621-2010-5623.
2The author was supported by the Scientific Committee of Kazakhstan’s Ministry of Education and Science, grant 0732/GF 2012–14.
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Sagitov, S., Shaimerdenova, A. Extinction times for a birth–death process with weak competition. Lith Math J 53, 220–234 (2013). https://doi.org/10.1007/s10986-013-9204-x
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DOI: https://doi.org/10.1007/s10986-013-9204-x