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arXiv · 2102.10572

Limit theorems on counting measures for a branching random walk with immigration in a random environment

Mengxue Li·Chuanmao Huang·Xiaoqiang Wang
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Abstract

We consider a branching random walk with immigration in a random environment, where the environment is a stationary and ergodic sequence indexed by time. We focus on the asymptotic properties of the sequence of measures $(Z_n)$ that count the number of particles of generation $n$ located in a Borel set of real line. In the present work, a series of limit theorems related to the above counting measures are established, including a central limit theorem, a moderate deviation principle and a large deviation result as well as a convergence theorem of the free energy.

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Mengxue Li, Chuanmao Huang, Xiaoqiang Wang. 2021-02-21. Limit theorems on counting measures for a branching random walk with immigration in a random environment. https://arxiv.org/abs/2102.10572

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