Central limit theorem for a critical multi-type branching process in random environment

Abstract

Let (Z n) n$\ge$0 with Z n = (Z n (i, j)) 1$\le$i,j$\le$p be a p multi-type 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 Zn |Mn| /|Z n | > 0 and ln Zn $\sqrt$ n /|Z n | > 0. These theorems extend similar results for single-type critical branching process in random environment.

References in corpus (1)

• Criticality for branching processes in random environment

Cited by in corpus (1)

• A conditioned local limit theorem for non-negative random matrices