Journal of Mathematical Sciences

, Volume 83, Issue 3, pp 397–400 | Cite as

Transition phenomena for a Galton-Watson process with immigration in a Markovian environment

  • E. E. Dyakonova


The behavior of a Galton-Watson process with state-dependent immigration in a Markovian random environment is investigated. We obtain a limit theorem in the near-critical case.


Limit Theorem Random Environment Transition Phenomenon Markovian Environment Markovian Random Environment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    W. L. Smith and W. E. Wilkinson, “On branching processes in random environments,”Ann. Math. Statist.,40, No. 3, 814–827 (1969).MathSciNetGoogle Scholar
  2. 2.
    K. B. Athreya and S. Karlin, “Branching processes with random environments, I. Extinction probabilities,”Ann. Math. Statist.,42, No. 5, 1499–1520 (1971).MathSciNetGoogle Scholar
  3. 3.
    K. B. Athreya and S. Karlin, “Branching processes with random environments, II. Limit theorems,”Ann. Math. Statist.,42, No. 6, 1843–1858 (1971).MathSciNetGoogle Scholar
  4. 4.
    E. E. Dyakonova, “On a Galton-Watson process with immigration,” in:Stability Problems for Stochastic Models. Proceedings of the Seminar [in Russian], The Institute for Systems Studies, Moscow (1991), pp. 49–52.Google Scholar
  5. 5.
    E. E. Dyakonova, “Transition phenomena for branching processes in random environment,”J. Math. Sciences (to appear) (1996).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • E. E. Dyakonova
    • 1
  1. 1.Steklov Mathematical InstituteMoscowRussia

Personalised recommendations