Abstract

Let ${\left(Z_n\right)}_{n\ge 0}$ with $Z_n={\left(Z_n\left(i,j\right)\right)}_{1\le i,j\le p}$ be a $p$ multitype critical branching process in random environment, and let $M_n$ be the expectation of $Z_n$ given a fixed environment. We prove theorems on convergence in distribution of sequences of branching processes $\left\{\left(Z_n∕\left|M_n\right|\right)\mid \left|Z_n\right|>0\right\}$ and $\left\{\left(ln{Z}_n∕\sqrt{n}\right)\mid \left|Z_n\right|>0\right\}$. These theorems extend similar results for single-type critical branching process in random environments.

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