Functional limit theorems for strongly subcritical branching processes in random environment

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:115

Article

Afanasyev, VI ; Geiger, J ; Kersting, G ; Vatutin, VA

关键词: branching process;    random environment;    random walk;    change of measure;    positive recurrent Markov chain;    functional limit theorem;   

DOI  :  10.1016/j.spa.2005.05.001

来源: Elsevier

【 摘 要 】

For a strongly subcritical branching process (Z(n))(n >= 0) in random environment the nonextinction probability at generation n decays at the same exponential rate as the expected generation size and given non-extinction at n the conditional distribution of Z(n) has a weak limit. Here we prove conditional functional limit theorems for the generation size process (Z(k))(0 <= k <= n) as well as for the random environment. We show that given the population survives up to generation n the environmental sequence still evolves in an i.i.d. fashion and that the conditioned generation size process converges in distribution to a positive recurrent Markov chain. (c) 2005 Elsevier B.V. All rights reserved.

【 授权许可】

Free