The limiting type of stationary distribution of a critical controlled branching process with immigration

IF 0.2 Q4 MATHEMATICS, APPLIED

Prikladnaya Diskretnaya Matematika Pub Date : 2023-01-01 DOI:10.4213/dm1776

Владимир Иванович Винокуров, V. Vinokurov

引用次数: 0

Abstract

Изучается последовательность $\{\xi_{n,t}\}_{t\geq1} $ регулируемых критических процессов с иммиграцией, где $n=1,2,…$ является некоторым целочисленным параметром, ограничивающим максимальный размер популяции. Показано, что при $n\rightarrow\infty $ стационарные распределения рассматриваемых ветвящихся процессов, нормированных величиной $ \sqrt{n}$, сходятся к распределению случайной величины, квадрат которой имеет гамма-распределение.

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具有迁移的临界控制分支过程平稳分布的极限类型

目前正在研究的是一系列受监管的移民危机审判，其中n= 1.2美元限制了人口的最大值。结果显示，在n / rightarrow / infty中，所考虑的分支过程的固定分布与分配伽马分布的随机变量的分布是一致的。

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

Prikladnaya Diskretnaya Matematika MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

50.00%

发文量

期刊介绍： The scientific journal Prikladnaya Diskretnaya Matematika has been issued since 2008. It was registered by Federal Control Service in the Sphere of Communications and Mass Media (Registration Witness PI № FS 77-33762 in October 16th, in 2008). Prikladnaya Diskretnaya Matematika has been selected for coverage in Clarivate Analytics products and services. It is indexed and abstracted in SCOPUS and WoS Core Collection (Emerging Sources Citation Index). The journal is a quarterly. All the papers to be published in it are obligatorily verified by one or two specialists. The publication in the journal is free of charge and may be in Russian or in English. The topics of the journal are the following: 1.theoretical foundations of applied discrete mathematics – algebraic structures, discrete functions, combinatorial analysis, number theory, mathematical logic, information theory, systems of equations over finite fields and rings; 2.mathematical methods in cryptography – synthesis of cryptosystems, methods for cryptanalysis, pseudorandom generators, appreciation of cryptosystem security, cryptographic protocols, mathematical methods in quantum cryptography; 3.mathematical methods in steganography – synthesis of steganosystems, methods for steganoanalysis, appreciation of steganosystem security; 4.mathematical foundations of computer security – mathematical models for computer system security, mathematical methods for the analysis of the computer system security, mathematical methods for the synthesis of protected computer systems;[...]