Galton–Watson Theta-Processes in a Varying Environment

Q3 Mathematics Stochastics and Quality Control Pub Date : 2024-01-15 DOI:10.1515/eqc-2024-0001

S. Sagitov, Yerakhmet Zhumayev

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Abstract

We consider a special class of Galton–Watson theta-processes in a varying environment fully defined by four parameters, with two of them ( θ , r )

{(\theta,r)}

being fixed over time n, and the other two ( a n , c n )

{(a_{n},c_{n})}

characterizing the altering reproduction laws. We establish a sequence of transparent limit theorems for the theta-processes with possibly defective reproduction laws. These results may serve as a stepping stone towards incisive general results for the Galton–Watson processes in a varying environment.

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变化环境中的加尔顿-沃森θ过程

我们考虑一类特殊的加尔顿-沃森 Theta 过程，它处于完全由四个参数定义的变化环境中，其中两个参数 ( θ , r ) {(\theta,r)} 在时间 n 上是固定的，另外两个 ( a n , c n ) {(a_{n},c_{n})}表征不断变化的再生产规律。我们为可能存在缺陷的再生产规律的θ过程建立了一系列透明极限定理。这些结果可以作为通向变化环境中加尔顿-沃森过程的精辟一般结果的垫脚石。

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

Stochastics and Quality Control Mathematics-Discrete Mathematics and Combinatorics

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1.10

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