Branching processes in random environment

Last modified: 2014-04-01

#### Abstract

A critical Galton-Watson branching process Z(n)in a random

environment e(n) ,n=0,1,... is considered. Assuming that {e(n)} is

an irreducible aperiodic positive recurrent Markov chain we prove,

as n tends to infinity a Yaglom-type conditional functional limit

theorem for the suitably normalized process {Z(nt),0<t<1} given

Z(n)>0. The statement we have proved generalizes several known

results for the critical branching processes in random environment

generated by a sequence of independent identically distributed

random variables.

environment e(n) ,n=0,1,... is considered. Assuming that {e(n)} is

an irreducible aperiodic positive recurrent Markov chain we prove,

as n tends to infinity a Yaglom-type conditional functional limit

theorem for the suitably normalized process {Z(nt),0<t<1} given

Z(n)>0. The statement we have proved generalizes several known

results for the critical branching processes in random environment

generated by a sequence of independent identically distributed

random variables.

#### Keywords

branching processes; random environment