Functional limit theorems for strongly subcritical branching processes in random environment

V.I. Afanasyev, J. Geiger, G. Kersting and V.A. Vatutin

Stochastic Processes and their Applications, 2005, vol. 115, issue 10, 1658-1676

Abstract: For a strongly subcritical branching process (Zn)n[greater-or-equal, slanted]0 in random environment the non-extinction 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 Zn has a weak limit. Here we prove conditional functional limit theorems for the generation size process (Zk)0[less-than-or-equals, slant]k[less-than-or-equals, slant]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.

Keywords: Branching; process; Random; environment; Random; walk; Change; of; measure; Positive; recurrent; Markov; chain; Functional; limit; theorem (search for similar items in EconPapers)
Date: 2005
References: View complete reference list from CitEc
Citations: View citations in EconPapers (9)

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