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 Diskr. Mat.: Year: Volume: Issue: Page: Find

 Diskr. Mat., 1997, Volume 9, Issue 1, Pages 30–42 (Mi dm453)

A branching process with migration in a random environment

E. E. D'yakonova

Abstract: We study a Galton–Watson branching process $Ż_n\}_{n=0}^\infty$ with migration in a random environment which is specified by a stationary Markov chain $\{\eta_n\}_{n=0}^\infty$ with finite state space. Let $f_{\eta_n}(z)$ be the offspring generating function of each particle of the $n$th generation, $M=\lim_{n\to\infty}\mathsf E\log f_{\eta_n}'(1)$.
It is proved that the stationary distribution of the properly normalized number of particles in the process $Ż_n\}_{n=0}^\infty$ converges to the uniform distribution on the interval $[0,1]$ as $M\to 1$.
The work was supported by the Russian Foundation for Basic Research, grant 96–01–00338 and INTAS–RFBR 95–0099.

DOI: https://doi.org/10.4213/dm453

Full text: PDF file (880 kB)

English version:
Discrete Mathematics and Applications, 1997, 7:1, 33–45

Bibliographic databases:

UDC: 519.2

Citation: E. E. D'yakonova, “A branching process with migration in a random environment”, Diskr. Mat., 9:1 (1997), 30–42; Discrete Math. Appl., 7:1 (1997), 33–45

Citation in format AMSBIB
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\by E.~E.~D'yakonova
\paper A branching process with migration in a random environment
\jour Diskr. Mat.
\yr 1997
\vol 9
\issue 1
\pages 30--42
\mathnet{http://mi.mathnet.ru/dm453}
\crossref{https://doi.org/10.4213/dm453}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1454177}
\zmath{https://zbmath.org/?q=an:0891.60083}
\transl
\jour Discrete Math. Appl.
\yr 1997
\vol 7
\issue 1
\pages 33--45