Asymptotic Behaviors for Critical Branching Processes with Immigration

2017/12/24 by Doudou Li, Mei Zhang, Li, Doudou +1
Mathematics · #Stochastic processes and statistical mechanics #Mathematical Dynamics and Fractals #Markov Chains and Monte Carlo Methods

paper · pdf · doi:10.48550/arxiv.1712.08892

Abstract

In this paper, we investigate the asymptotic behaviors of the critical branching process with immigration \Z_n, n≥ 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≤ i≤ n} Z_i is obtained.

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