Berry-Esseen's bound and harmonic moments for supercritical multi-type branching processes in random environments

Grama Ion (1) , Quansheng Liu (1) , Erwan Pin (1)

1 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

Consider a supercritical multi-type branching process in an independent and identically distributed random environment. We establish a Berry-Esseen type bound for the rate of convergence in the central limit theorem on the population size at time n as n goes to infinity. To this end we first find simple conditions for the existence of harmonic moments of the limit variable of the fundamental martingale.

Mots clés: Multitype branching processes; Random environments; Berry-Essenn's bound; harmonic moments; products of random matrices

Domaines: Probabilités [math.PR]

Grama Ion, Quansheng Liu, Erwan Pin. Berry-Esseen's bound and harmonic moments for supercritical multi-type branching processes in random environments. 2020. ⟨hal-02911865⟩