Precise large deviation estimates for branching process in random environment

2017/06/13 by Dariusz Buraczewski, Buraczewski, Dariusz, Piotr Dyszewski +1
Mathematics · Medicine · Economics, Econometrics and Finance · #Stochastic processes and statistical mechanics #Mathematical and Theoretical Epidemiology and Ecology Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1706.03874

Abstract

We consider the branching process in random environment \Z_n\_{n≥ 0}, which is a~population growth process where individuals reproduce independently of each other with the reproduction law randomly picked at each generation. We describe precise asymptotics of upper large deviations, i.e. ℙ[Z_n > e^ρn]. Moreover in the subcritical case, under the Cramér condition on the mean of the reproduction law, we investigate large deviations-type estimates for the first passage time of the branching process in question and its total population size.

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• Large deviations for Branching Processes in Random Environment
• Upper large deviations for Branching Processes in Random Environment with heavy tails
• Lower large deviations for supercritical branching processes in random environment
• Limit theorems for supercritical branching processes in random environment
• Berry-Esseen's bound and Cramér's large deviation expansion for a supercritical branching process in a random environment