Central limit theorem for a critical multitype branching process in random environments

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 and . These theorems extend similar results for single-type critical branching process in random environments.