BERRY-ESSEEN BOUND AND PRECISE MODERATE DEVIATIONS FOR BRANCHING RANDOM WALKS WITH PRODUCTS OF RANDOM MATRICES
Résumé
We consider a branching random walk where particles give birth to children as a Galton-Watson process, which move in $ \mathbb R^d $ according to products of independent and identically distributed random matrices. We establish a Berry-Esseen bound and a Cramér type moderate deviation expansion for the counting measure which counts the number of particles in generation $n$ situated in a region, as $ n \rightarrow \infty $. In the proof, we construct a new martingale, and establish its uniform convergence as well as that of the fundamental martingale.
Domaines
Probabilités [math.PR]Origine | Fichiers produits par l'(les) auteur(s) |
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