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Some properties of branching processes with random control functions and affected by viral infectivity in random environments
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 som...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer International Publishing
2023
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10184110/ https://www.ncbi.nlm.nih.gov/pubmed/37216170 http://dx.doi.org/10.1186/s13662-023-03775-3 |
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author | Ren, Min Zhang, Guanghui |
author_facet | Ren, Min Zhang, Guanghui |
author_sort | Ren, Min |
collection | PubMed |
description | 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 [Formula: see text] , the normalization processes [Formula: see text] are studied, and the sufficient conditions of [Formula: see text] a.s., [Formula: see text] and [Formula: see text] 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 [Formula: see text] , the normalization processes [Formula: see text] are studied, and the sufficient conditions of [Formula: see text] a.s., and [Formula: see text] convergence are obtained. |
format | Online Article Text |
id | pubmed-10184110 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | Springer International Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-101841102023-05-16 Some properties of branching processes with random control functions and affected by viral infectivity in random environments Ren, Min Zhang, Guanghui Adv Contin Discret Model Research 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 [Formula: see text] , the normalization processes [Formula: see text] are studied, and the sufficient conditions of [Formula: see text] a.s., [Formula: see text] and [Formula: see text] 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 [Formula: see text] , the normalization processes [Formula: see text] are studied, and the sufficient conditions of [Formula: see text] a.s., and [Formula: see text] convergence are obtained. Springer International Publishing 2023-05-15 2023 /pmc/articles/PMC10184110/ /pubmed/37216170 http://dx.doi.org/10.1186/s13662-023-03775-3 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Research Ren, Min Zhang, Guanghui Some properties of branching processes with random control functions and affected by viral infectivity in random environments |
title | Some properties of branching processes with random control functions and affected by viral infectivity in random environments |
title_full | Some properties of branching processes with random control functions and affected by viral infectivity in random environments |
title_fullStr | Some properties of branching processes with random control functions and affected by viral infectivity in random environments |
title_full_unstemmed | Some properties of branching processes with random control functions and affected by viral infectivity in random environments |
title_short | Some properties of branching processes with random control functions and affected by viral infectivity in random environments |
title_sort | some properties of branching processes with random control functions and affected by viral infectivity in random environments |
topic | Research |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10184110/ https://www.ncbi.nlm.nih.gov/pubmed/37216170 http://dx.doi.org/10.1186/s13662-023-03775-3 |
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