English

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

Probability 2021-02-23 v1

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 (Zn)(Z_n) that count the number of particles of generation nn 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.

Keywords

Cite

@article{arxiv.2102.10572,
  title  = {Limit theorems on counting measures for a branching random walk with immigration in a random environment},
  author = {Mengxue Li and Chuanmao Huang and Xiaoqiang Wang},
  journal= {arXiv preprint arXiv:2102.10572},
  year   = {2021}
}