Some properties of branching processes with random control functions and affected by viral infectivity in random environments.

Min Ren, Guanghui Zhang
{"title":"Some properties of branching processes with random control functions and affected by viral infectivity in random environments.","authors":"Min Ren,&nbsp;Guanghui Zhang","doi":"10.1186/s13662-023-03775-3","DOIUrl":null,"url":null,"abstract":"<p><p>In this paper, a model of branching processes with random control functions and affected by viral infectivity in independent and identically distributed random environments is established, and the Markov property of the model and a sufficient condition for the model to be certainly extinct under some conditions are discussed. Then, the limit properties of the model are studied. Under the normalization factor <math><mo>{</mo><msub><mi>S</mi><mi>n</mi></msub><mo>:</mo><mi>n</mi><mo>∈</mo><mi>N</mi><mo>}</mo></math>, the normalization processes <math><mo>{</mo><msub><mover><mi>W</mi><mo>ˆ</mo></mover><mi>n</mi></msub><mo>:</mo><mi>n</mi><mo>∈</mo><mi>N</mi><mo>}</mo></math> are studied, and the sufficient conditions of <math><mo>{</mo><msub><mover><mi>W</mi><mo>ˆ</mo></mover><mi>n</mi></msub><mo>:</mo><mi>n</mi><mo>∈</mo><mi>N</mi><mo>}</mo></math> a.s., <math><msup><mi>L</mi><mn>1</mn></msup></math> and <math><msup><mi>L</mi><mn>2</mn></msup></math> convergence are given; A sufficient condition and a necessary condition for convergence to a nondegenerate at zero random variable are obtained. Under the normalization factor <math><mo>{</mo><msub><mi>I</mi><mi>n</mi></msub><mo>:</mo><mi>n</mi><mo>∈</mo><mi>N</mi><mo>}</mo></math>, the normalization processes <math><mo>{</mo><msub><mover><mi>W</mi><mo>¯</mo></mover><mi>n</mi></msub><mo>:</mo><mi>n</mi><mo>∈</mo><mi>N</mi><mo>}</mo></math> are studied, and the sufficient conditions of <math><mo>{</mo><msub><mover><mi>W</mi><mo>¯</mo></mover><mi>n</mi></msub><mo>:</mo><mi>n</mi><mo>∈</mo><mi>N</mi><mo>}</mo></math> a.s., and <math><msup><mi>L</mi><mn>1</mn></msup></math> convergence are obtained.</p>","PeriodicalId":72091,"journal":{"name":"Advances in continuous and discrete models","volume":"2023 1","pages":"26"},"PeriodicalIF":2.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10184110/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in continuous and discrete models","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1186/s13662-023-03775-3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

Abstract

In this paper, a model of branching processes with random control functions and affected by viral infectivity in independent and identically distributed random environments is established, and the Markov property of the model and a sufficient condition for the model to be certainly extinct under some conditions are discussed. Then, the limit properties of the model are studied. Under the normalization factor {Sn:nN}, the normalization processes {Wˆn:nN} are studied, and the sufficient conditions of {Wˆn:nN} a.s., L1 and L2 convergence are given; A sufficient condition and a necessary condition for convergence to a nondegenerate at zero random variable are obtained. Under the normalization factor {In:nN}, the normalization processes {W¯n:nN} are studied, and the sufficient conditions of {W¯n:nN} a.s., and L1 convergence are obtained.

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
随机环境中受病毒感染性影响的具有随机控制函数的分支过程的一些性质。
本文建立了独立同分布随机环境中受病毒感染的具有随机控制函数的分支过程模型,讨论了该模型的马尔可夫性质和在某些条件下该模型肯定绝灭的充分条件。然后,研究了模型的极限性质。在归一化因子{Sn:n∈n}下,研究了归一化过程{W′n:n∈n},并给出了{W′n:n∈n} as、L1、L2收敛的充分条件;得到了在零随机变量处收敛到非退化的充分条件和必要条件。在归一化因子{In:n∈n}下,研究了归一化过程{W¯n:n∈n},得到了{W¯n:n∈n} a.s.和L1收敛的充分条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
2.30
自引率
0.00%
发文量
0
期刊最新文献
Conservative Fourier spectral method for a class of modified Zakharov system with high-order space fractional quantum correction Universal approximation property of a continuous neural network based on a nonlinear diffusion equation Adaptive neural-domain refinement for solving time-dependent differential equations Bifurcation and chaos in a discrete Holling–Tanner model with Beddington–DeAngelis functional response Stability and dynamics of a stochastic discrete fractional-order chaotic system with short memory
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1