Asymptotic properties of branching processes in random environment (Q2711894)

This paper provides very general asymptotic results for subcritical, critical and supercritical cases of the branching process \(\{Z_n\}\) in a random environment. In the first two cases these concern the behaviour of \([P(Z_n > 0)]^{1/n}\) in the context of a stationary and ergodic random environment and conditions under which the limit exists. For the critical and supercritical cases and for independent and identically distributed environments there are also results on the limit behaviour of \(P(Z_n > 0)\).