Lithuanian Mathematical Journal

, Volume 53, Issue 2, pp 220–234 | Cite as

Extinction times for a birth–death process with weak competition

  • Serik Sagitov
  • Altynay Shaimerdenova


We consider a birth–death process with birth rates and death rates +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). 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.


birth–death process carrying capacity time to extinction coupling method logistic branching process 




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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Mathematical SciencesChalmers University of Technology and University of GothenburgGothenburgSweden
  2. 2.Al-Farabi Kazakh National UniversityAlmatyKazakhstan

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