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2 results

  • CONDITIONS FOR RECURRENCE AND TRANSIENCE FOR TIME-INHOMOGENEOUS BIRTH-AND-DEATH PROCESSES

  • Part of
  • VYACHESLAV M. ABRAMOV
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 109 / Issue 2 / April 2024
    Published online by Cambridge University Press:
    23 June 2023, pp. 393-402
    Print publication:
    April 2024
    • Article
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  • We derive conditions for recurrence and transience for time-inhomogeneous birth-and-death processes considered as random walks with positively biased drifts. We establish a general result, from which the earlier known particular results by Menshikov and Volkov [‘Urn-related random walk with drift $\rho x^\alpha /t^\beta $’, Electron. J. Probab. 13 (2008), 944–960] follow.

  • On supercritical branching processes with emigration

  • Part of
  • Georg Braun
  • Journal:
    Journal of Applied Probability / Volume 59 / Issue 3 / September 2022
    Published online by Cambridge University Press:
    08 July 2022, pp. 734-754
    Print publication:
    September 2022

  • We study supercritical branching processes under the influence of an independent and identically distributed (i.i.d.) emigration component. We provide conditions under which the lifetime of the process is finite or has a finite expectation. A theorem of Kesten–Stigum type is obtained, and the extinction probability for a large initial population size is related to the tail behaviour of the emigration.