Cramér type moderate deviation expansion for a supercritical multi-type branching process in a random environment
Résumé
Let $Z_n^i=(Z_n^i(1), \cdots, Z_n^i(d)),\,n\geq 0,$ be a supercritical $d$-type branching process in an independent and identically distributed random environment $\xi =(\xi_0, \xi_1, \cdots)$, starting with one initial particle of type $i$.
We establish a Cram\'er type moderate deviation expansion for $\log\|Z_n^i\|$.
To this end, we first prove uniform results for the existence of harmonic moments and Berry-Esseen type bound under suitably changed measure, using the spectral gap theory on products of random matrices and the fundamental martingale that we found in an earlier paper.
Origine : Fichiers produits par l'(les) auteur(s)
Loading...