随机环境下具有迁移的强超临界分支过程的极限定理

Q3 Mathematics

Stochastics and Quality Control Pub Date : 2021-11-17 DOI:10.1515/eqc-2021-0036

V. Afanasyev

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引用次数: 0

摘要

摘要考虑一个随机环境下的强超临界分支过程，迁移过程在很远的时间𝑛停止。假定每一代后代的繁殖规律是几何的。该过程是在时间𝑛后其消失的条件下考虑的。证明了该过程的两个极限定理:第一个定理适用于从0到𝑛的时间区间，第二个定理适用于𝑛到+∞+ \infty的时间区间。

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Limit Theorems for a Strongly Supercritical Branching Process with Immigration in Random Environment

Abstract We consider a strongly supercritical branching process in random environment with immigration stopped at a distant time 𝑛. The offspring reproduction law in each generation is assumed to be geometric. The process is considered under the condition of its extinction after time 𝑛. Two limit theorems for this process are proved: the first one is for the time interval from 0 till 𝑛, and the second one is for the time interval from 𝑛 till + ∞ +\infty .

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来源期刊

Stochastics and Quality Control Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.10

自引率

0.00%

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