Reduced multitype critical branching processes in random environment

Elena E. D'yakonova

Diskretnaya Matematika, Tome 28 (2016) no. 4, pp. 58-79.

Résumé

We consider a multitype critical branching process $\mathbf{Z}_{n},n=0,1,...$, in an i.i.d. random environment. Let $Z_{m,n}$ be the number of particles in this process at time $m$ having descendants at time $n$. A limit theorem is proved for the logarithm of $Z_{nt,n}$ at moments $nt,\,0\leq t\leq 1,$ conditioned on the survival of the process $\mathbf{Z}_{n}$ up to moment $n$ when $n\rightarrow \infty $.

Détail

Keywords: multitupe branching processes, reduced branching processes, random environment.

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