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

2021/02/21 by Li, Mengxue, Huang, Chuanmao, Wang, Xiaoqiang
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2102.10572

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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