Comparison on the criticality parameters for two supercritical branching processes in random environments

Abstract

Let {Z 1,n , n ≥ 0} and {Z 2,n , n ≥ 0} be two supercritical branching processes in different random environments, with criticality parameters µ 1 and µ 2 respectively. It is known thatIn this paper, we are interested in the comparison on the two criticality parameters. To this end, we prove a non-uniform Berry-Esseen's bound and Cramér's moderate deviations for 1 n ln Z 1,n − 1 m ln Z 2,m as m, n → ∞. An application is also given for constructing confidence interval for µ 1 − µ 2 .