Limit theorem for stationary distribution of a critical controlled branching process with immigration

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2023-10-01 DOI:10.1515/dma-2023-0030

Vladimir I. Vinokurov

引用次数: 0

Abstract

Abstract We consider the sequence {ξn,t}t≥1 of controlled critical branching processes with immigration, where n = 1, 2, … is an integer parameter limiting the population size. It is shown that for n → ∞ the stationary distributions of considered branching processes normalized by n $\begin{array}{} \sqrt{n} \end{array} $ converge to the distribution of a random variable whose square has a gamma distribution.

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有移民的临界受控分支过程静态分布的极限定理

摘要我们考虑了有移民的受控临界分支过程序列{ξn,t}t≥1，其中n = 1, 2, ...是限制种群规模的整数参数。研究表明，对于 n → ∞，所考虑的分支过程的静态分布以 n $\begin{array}{} 归一化。\sqrt{n}\end{array} $ 收敛到其平方具有伽马分布的随机变量的分布。

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

Discrete Mathematics and Applications MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

20.00%

发文量

期刊介绍： The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.