Moments and asymptotic properties for supercritical branching processes with immigration in random environments

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Stochastic Models Pub Date : 2022-02-23 DOI:10.1080/15326349.2022.2040365

Chunmao Huang, Chen Wang, Xiaoqiang Wang

引用次数: 1

Abstract

Abstract We consider a supercritical discrete-time branching process with immigration Y in a stationary and ergodic environment ξ. Let mn be the mean of the reproduction distribution at time n conditioned on the environment ξ and be the natural submartingale of the model. We show sufficient conditions for the boundedness of the moments and for and discover the exponential Lp decay rates of as well as the rates of Then, as an application of the moment results, we show the exponential decay rates of and the convergence rates of the average of ratios

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随机环境中具有迁移的超临界分支过程的矩和渐近性质

考虑平稳遍历环境ξ中具有Y迁移的超临界离散分支过程。设mn为条件为ξ的n时刻的再生产分布的均值，为模型的自然次幂。我们给出了矩的有界性的充分条件，并发现了矩的指数衰减率和指数衰减率，作为矩结果的应用，我们给出了比率的指数衰减率和平均值的收敛率

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Stochastic Models 数学-统计学与概率论

CiteScore

1.30

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastic Models publishes papers discussing the theory and applications of probability as they arise in the modeling of phenomena in the natural sciences, social sciences and technology. It presents novel contributions to mathematical theory, using structural, analytical, algorithmic or experimental approaches. In an interdisciplinary context, it discusses practical applications of stochastic models to diverse areas such as biology, computer science, telecommunications modeling, inventories and dams, reliability, storage, queueing theory, mathematical finance and operations research.