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

Mengxue Li, Xiaoqiang Wang, Chuanmao Huang

Publication date: 21 February 2021

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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