具有小漂移的随机漫步的运行最大值的边界

Pub Date : 2020-10-17 DOI:10.30757/alea.v19-03

Ofer Busani, T. Seppalainen

{"title":"具有小漂移的随机漫步的运行最大值的边界","authors":"Ofer Busani, T. Seppalainen","doi":"10.30757/alea.v19-03","DOIUrl":null,"url":null,"abstract":"We derive a lower bound for the probability that a random walk with i.i.d.\\ increments and small negative drift $\\mu$ exceeds the value $x>0$ by time $N$. When the moment generating functions are bounded in an interval around the origin, this probability can be bounded below by $1-O(x|\\mu| \\log N)$. The approach is elementary and does not use strong approximation theorems.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Bound on the running maximum of a random walk with small drift\",\"authors\":\"Ofer Busani, T. Seppalainen\",\"doi\":\"10.30757/alea.v19-03\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We derive a lower bound for the probability that a random walk with i.i.d.\\\\ increments and small negative drift $\\\\mu$ exceeds the value $x>0$ by time $N$. When the moment generating functions are bounded in an interval around the origin, this probability can be bounded below by $1-O(x|\\\\mu| \\\\log N)$. The approach is elementary and does not use strong approximation theorems.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2020-10-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.30757/alea.v19-03\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.30757/alea.v19-03","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 2

摘要

我们推导了一个概率的下界，即具有i.i.d增量和小负漂移$\mu$的随机漫步在时间$N$上超过$x>0$的值。当矩生成函数在原点附近的一个区间内有界时，这个概率可以用$1-O(x|\mu| \log N)$为界。该方法是初等的，不使用强逼近定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

Bound on the running maximum of a random walk with small drift

We derive a lower bound for the probability that a random walk with i.i.d.\ increments and small negative drift $\mu$ exceeds the value $x>0$ by time $N$. When the moment generating functions are bounded in an interval around the origin, this probability can be bounded below by $1-O(x|\mu| \log N)$. The approach is elementary and does not use strong approximation theorems.

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