BERRY-ESSEEN'S BOUND AND CRAMÉR'S LARGE DEVIATION EXPANSION FOR A SUPERCRITICAL BRANCHING PROCESS IN A RANDOM ENVIRONMENT
Résumé
Let (Z n) be a supercritical branching process in a random environment ξ = (ξ n). We establish a Berry-Esseen bound and a Cramér's type large deviation expansion for log Z n under the annealed law P. We also improve some earlier results about the harmonic moments of the limit variable W = lim n→∞ W n , where W n = Z n /E ξ Z n is the normalized population size.
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