Rademacher级数的递归性与短暂性

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
Satyaki Bhattacharya, S. Volkov
{"title":"Rademacher级数的递归性与短暂性","authors":"Satyaki Bhattacharya, S. Volkov","doi":"10.30757/alea.v20-03","DOIUrl":null,"url":null,"abstract":"We introduce the notion of {\\bf a}-walk $S(n)=a_1 X_1+\\dots+a_n X_n$, based on a sequence of positive numbers ${\\bf a}=(a_1,a_2,\\dots)$ and a Rademacher sequence $X_1,X_2,\\dots$. We study recurrence/transience (properly defined) of such walks for various sequences of ${\\bf a}$. In particular, we establish the classification in the cases where $a_k=\\lfloor k^\\beta\\rfloor$, $\\beta>0$, as well as in the case $a_k=\\lceil \\log_\\gamma k \\rceil$ or $a_k=\\log_\\gamma k$ for $\\gamma>1$.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Recurrence and transience of Rademacher series\",\"authors\":\"Satyaki Bhattacharya, S. Volkov\",\"doi\":\"10.30757/alea.v20-03\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce the notion of {\\\\bf a}-walk $S(n)=a_1 X_1+\\\\dots+a_n X_n$, based on a sequence of positive numbers ${\\\\bf a}=(a_1,a_2,\\\\dots)$ and a Rademacher sequence $X_1,X_2,\\\\dots$. We study recurrence/transience (properly defined) of such walks for various sequences of ${\\\\bf a}$. In particular, we establish the classification in the cases where $a_k=\\\\lfloor k^\\\\beta\\\\rfloor$, $\\\\beta>0$, as well as in the case $a_k=\\\\lceil \\\\log_\\\\gamma k \\\\rceil$ or $a_k=\\\\log_\\\\gamma k$ for $\\\\gamma>1$.\",\"PeriodicalId\":49244,\"journal\":{\"name\":\"Alea-Latin American Journal of Probability and Mathematical Statistics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2022-05-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"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.v20-03\",\"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.v20-03","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: 0

摘要

基于正数序列${\bf a}=(a_1,a_2,\dots)$和Rademacher序列$X_1,X_2,\dots$,我们引入了行走$S(n)=a_1X_1+\dots+a_nX_n$的概念。我们研究了${\bf a}$的各种序列的这种行走的递推/瞬态(正确定义)。特别是,我们在$a_k=\lfloor k^\beta\rfloor$,$\beta>0$的情况下,以及在$a_k=\lceil\log_\gamma k\rceil$或$a_k=\log_\ gamma k$的情况中,为$\gamma>1$建立分类。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Recurrence and transience of Rademacher series
We introduce the notion of {\bf a}-walk $S(n)=a_1 X_1+\dots+a_n X_n$, based on a sequence of positive numbers ${\bf a}=(a_1,a_2,\dots)$ and a Rademacher sequence $X_1,X_2,\dots$. We study recurrence/transience (properly defined) of such walks for various sequences of ${\bf a}$. In particular, we establish the classification in the cases where $a_k=\lfloor k^\beta\rfloor$, $\beta>0$, as well as in the case $a_k=\lceil \log_\gamma k \rceil$ or $a_k=\log_\gamma k$ for $\gamma>1$.
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