Limit theorems for supercritical branching processes in random environment

Dariusz Buraczewski; Ewa Damek

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arXiv · 2007.00443

Limit theorems for supercritical branching processes in random environment

Dariusz Buraczewski·Ewa Damek

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Abstract

We consider the branching process in random environment $\{Z_n\}_{n\geq 0}$, 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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BibTeX RIS

Dariusz Buraczewski, Ewa Damek. 2020-07-01. Limit theorems for supercritical branching processes in random environment. https://arxiv.org/abs/2007.00443

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