Large deviations of branching processes with immigration in random environment

被引：8

作者：

Dmitruschenkov D.V. ^{[1
]}

Shklyaev A.V. ^{[1
]}

机构：

[1] Moscow State University, Russia

来源：

Discrete Mathematics and Applications | 2017年 / 27卷 / 06期

基金：

俄罗斯基础研究基金会;

关键词：

Branching processes; Cramr condition; Large deviations; Processes with immigration; Random environments; Random walks;

D O I：

10.1515/dma-2017-0037

中图分类号：

O211 [概率论（几率论、或然率论）];

学科分类号：

摘要：

We consider branching process Zn in random environment such that the associated random walk Sn has increments ξi with mean μ and satisfy the Cramér condition Eehξi < ∞, 0 < h < h+. Let Xi be the number of particles immigrating into the -th generation of the process, ehhXi < ∞, 0 < < +. We suppose that the number of offsprings of one particle conditioned on the environment has the geometric distribution. It is shown that the supplement of immigration to critical or supercritical processes results only in the change of multiplicative constant in the asymptotics of large deviation probabilities P Zn ≥ exp(θn)}, θ > μ. In the case of subcritical processes analogous result is obtained for θ > γ, where γ > 0 is some constant. For all constants explicit formulas are given.

引用

页码：361 / 376

页数：15

共 8 条

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