Asymptotic Behaviors for Critical Branching Processes with Immigration

Doudou Li; Mei Zhang

Asymptotic Behaviors for Critical Branching Processes with Immigration

Probability 2017-12-27 v1

Authors: Doudou Li , Mei Zhang

Abstract

In this paper, we investigate the asymptotic behaviors of the critical branching process with immigration $\{Z_n, n\ge 0\}$ . First we get some estimation for the probability generating function of $Z_n$ . Based on it, we get a large deviation for $Z_{n+1}/Z_n$ . Lower and upper deviations for $Z_n$ are also studied. As a by-product, an upper deviation for $\max_{1\le i\le n} Z_i$ is obtained.

Keywords

critical branching process immigration probability generating function large deviation upper deviation lower deviation

Cite

@article{arxiv.1712.08892,
  title  = {Asymptotic Behaviors for Critical Branching Processes with Immigration},
  author = {Doudou Li and Mei Zhang},
  journal= {arXiv preprint arXiv:1712.08892},
  year   = {2017}
}

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