细胞大小有界的生长碎裂过程的强数定律

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
E. Horton, A. Watson
{"title":"细胞大小有界的生长碎裂过程的强数定律","authors":"E. Horton, A. Watson","doi":"10.30757/ALEA.v19-68","DOIUrl":null,"url":null,"abstract":"Growth-fragmentation processes model systems of cells that grow continuously over time and then fragment into smaller pieces. Typically, on average, the number of cells in the system exhibits asynchronous exponential growth and, upon compensating for this, the distribution of cell sizes converges to an asymptotic profile. However, the long-term stochastic behaviour of the system is more delicate, and its almost sure asymptotics have been so far largely unexplored. In this article, we study a growth-fragmentation process whose cell sizes are bounded above, and prove the existence of regimes with differing almost sure long-term behaviour.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2020-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Strong laws of large numbers for a growth-fragmentation process with bounded cell sizes\",\"authors\":\"E. Horton, A. Watson\",\"doi\":\"10.30757/ALEA.v19-68\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Growth-fragmentation processes model systems of cells that grow continuously over time and then fragment into smaller pieces. Typically, on average, the number of cells in the system exhibits asynchronous exponential growth and, upon compensating for this, the distribution of cell sizes converges to an asymptotic profile. However, the long-term stochastic behaviour of the system is more delicate, and its almost sure asymptotics have been so far largely unexplored. In this article, we study a growth-fragmentation process whose cell sizes are bounded above, and prove the existence of regimes with differing almost sure long-term behaviour.\",\"PeriodicalId\":49244,\"journal\":{\"name\":\"Alea-Latin American Journal of Probability and Mathematical Statistics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2020-12-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Alea-Latin American Journal of Probability and Mathematical Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.30757/ALEA.v19-68\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Alea-Latin American Journal of Probability and Mathematical Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.30757/ALEA.v19-68","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 1

摘要

生长-分裂过程模拟细胞系统,随着时间的推移不断生长,然后分裂成更小的碎片。通常,平均而言,系统中的细胞数量呈现异步指数增长,并且在补偿这一点后,细胞大小的分布收敛于渐近轮廓。然而,该系统的长期随机行为更为微妙,其几乎肯定的渐近性迄今在很大程度上尚未得到探索。在本文中,我们研究了一个细胞大小有界的生长-分裂过程,并证明了具有不同的几乎确定的长期行为的制度的存在。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Strong laws of large numbers for a growth-fragmentation process with bounded cell sizes
Growth-fragmentation processes model systems of cells that grow continuously over time and then fragment into smaller pieces. Typically, on average, the number of cells in the system exhibits asynchronous exponential growth and, upon compensating for this, the distribution of cell sizes converges to an asymptotic profile. However, the long-term stochastic behaviour of the system is more delicate, and its almost sure asymptotics have been so far largely unexplored. In this article, we study a growth-fragmentation process whose cell sizes are bounded above, and prove the existence of regimes with differing almost sure long-term behaviour.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
1.10
自引率
0.00%
发文量
48
期刊介绍: ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted. ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper. ALEA is affiliated with the Institute of Mathematical Statistics.
×
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
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信