Central limit theorems for a supercritical branching process in a random environment
Résumé
For a supercritical branching process $(Z_n)$ in a stationary and ergodic environment $\xi$, we study the rate of convergence of the normalized population $W_n= Z_n/E[Z_n|\xi]$ to its limit $W_\infty$: we show a central limit theorem for $W_{\infty}-W_n$ with suitable normalization and derive a Berry-Esseen bound for the rate of convergence in the central limit theorem when the environment is independent and identically distributed. Similar results are also shown for $W_{n+k}-W_n$ for each fixed $k \in \mathbb{N}^*$.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)
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