Limit theorems for supercritical branching processes in random environment

2020/07/01 by Dariusz Buraczewski, Buraczewski, Dariusz, Ewa Damek +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2007.00443

openalex publication_date 2020/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 focus on the supercritical case, when the process survives with a positive probability and grows exponentially fast on the nonextinction set. Our main is goal is establish Fourier techniques for this model, which allow to obtain a number of precise estimates related to limit theorems. As a consequence we provide new results concerning central limit theorem, Edgeworth expansions and renewal theorem for log Z_n.

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