We consider a branching process (Z(n)) in a stationary and ergodic random environment xi = (xi(n)). Athreya and Karlin (1971) proved the basic result about the concept of subcriticality and criticality, by showing that under the quenched law P-xi , the conditional distribution of Z(n) given the non-extinction at time n converges in law to a proper distribution on N+ = {1, 2,. . .} in the subcritical case, and to the null distribution in the critical case, under the condition that the environment sequence is exchangeable. In this paper we first improve this basic result by removing the exchange...
