On asymptotic structure of critical Galton-Watson branching processes allowing immigration with infinite variance

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Stochastic Models Pub Date : 2022-02-21 DOI:10.1080/15326349.2022.2033628

A. Imomov, E. E. Tukhtaev

引用次数: 1

Abstract

Abstract We consider the Galton-Watson branching process allowing immigration. We are dealing with the critical case, in which the immigration law has infinite mean and the offspring law have an infinite variance. An explicit-integral form of the generating function of a stationary measure for the process without immigration is found. We study the asymptotic properties of transition probabilities and their convergence to stationary measures in the case of processes with immigration, when the process is ergodic. And also we define a rate of speed of this convergence.

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允许无限方差移民的临界Galton—Watson分支过程的渐近结构

我们考虑允许移民的高尔顿-沃森分支过程。我们正在处理的是一种临界情况，其中移民法有无限的均值，而后代法有无限的方差。给出了无迁移过程平稳测度生成函数的显式积分形式。研究了当过程是遍历时，具有迁移的过程的转移概率的渐近性质及其向平稳测度的收敛性。我们还定义了收敛的速度。

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.