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

Let (Z n) n≥0 with Z n = (Z n (i, j)) 1≤i,j≤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 √ n /|Z n | > 0. These theorems extend similar results for single-type critical branching process in random environment.