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Moments, moderate and large deviations for a branching process in a random environment
- Source :
- Stochastic Processes and their Applications 122 (2012) 522-545
- Publication Year :
- 2010
-
Abstract
- Let $(Z_{n})$ be a supercritical branching process in a random environment $\xi $, and $W$ be the limit of the normalized population size $Z_{n}/\mathbb{E}[Z_{n}|\xi ]$. We show large and moderate deviation principles for the sequence $\log Z_{n}$ (with appropriate normalization). For the proof, we calculate the critical value for the existence of harmonic moments of $W$, and show an equivalence for all the moments of $Z_{n}$. Central limit theorems on $W-W_n$ and $\log Z_n$ are also established.
- Subjects :
- Mathematics - Probability
60J80, 60K37, 60F10
Subjects
Details
- Database :
- arXiv
- Journal :
- Stochastic Processes and their Applications 122 (2012) 522-545
- Publication Type :
- Report
- Accession number :
- edsarx.1007.1738
- Document Type :
- Working Paper