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Berry-Esseen's bound and Cram\'er's large deviation expansion for a supercritical branching process in a random environment
- Publication Year :
- 2016
-
Abstract
- Let $(Z_n)$ be a supercritical branching process in a random environment $\xi = (\xi_n)$. We establish a Berry-Esseen bound and a Cram\'er's type large deviation expansion for $\log Z_n$ under the annealed law $\mathbb P$. We also improve some earlier results about the harmonic moments of the limit variable $W=lim_{n\to \infty} W_n$, where $W_n =Z_n/ \mathbb{E}_{\xi} Z_n$ is the normalized population size.
- Subjects :
- Mathematics - Probability
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1602.02081
- Document Type :
- Working Paper