重尾复合更新过程和莱维过程在随机时间间隔内的最大值

IF 1.1 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications Pub Date : 2024-06-25 DOI:10.1016/j.spa.2024.104422

Sergey Foss , Dmitry Korshunov , Zbigniew Palmowski

{"title":"重尾复合更新过程和莱维过程在随机时间间隔内的最大值","authors":"Sergey Foss , Dmitry Korshunov , Zbigniew Palmowski","doi":"10.1016/j.spa.2024.104422","DOIUrl":null,"url":null,"abstract":"<div>We derive subexponential tail asymptotics for the distribution of the maximum of a compound renewal process with linear component and of a Lévy process, both with negative drift, over random time horizon <math><mi>τ</mi></math> that does not depend on the future increments of the process. Our asymptotic results are uniform over the whole class of such random times. Particular examples are given by stopping times and by <math><mi>τ</mi></math> independent of the processes. We link our results with random walk theory.</div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"176 ","pages":"Article 104422"},"PeriodicalIF":1.1000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Maxima over random time intervals for heavy-tailed compound renewal and Lévy processes\",\"authors\":\"Sergey Foss , Dmitry Korshunov , Zbigniew Palmowski\",\"doi\":\"10.1016/j.spa.2024.104422\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>We derive subexponential tail asymptotics for the distribution of the maximum of a compound renewal process with linear component and of a Lévy process, both with negative drift, over random time horizon <math><mi>τ</mi></math> that does not depend on the future increments of the process. Our asymptotic results are uniform over the whole class of such random times. Particular examples are given by stopping times and by <math><mi>τ</mi></math> independent of the processes. We link our results with random walk theory.</div>\",\"PeriodicalId\":51160,\"journal\":{\"name\":\"Stochastic Processes and their Applications\",\"volume\":\"176 \",\"pages\":\"Article 104422\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2024-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Stochastic Processes and their Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0304414924001285\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastic Processes and their Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0304414924001285","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 0

摘要

我们推导了具有线性成分的复合更新过程和具有负漂移的莱维过程的最大值在不依赖于过程未来增量的时间跨度上的亚指数尾部渐近分布。我们的渐近结果涵盖了所有这类随机时间。我们给出了停止时间和独立过程的具体例子。我们将我们的结果与随机漫步理论联系起来。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Maxima over random time intervals for heavy-tailed compound renewal and Lévy processes

We derive subexponential tail asymptotics for the distribution of the maximum of a compound renewal process with linear component and of a Lévy process, both with negative drift, over random time horizon $τ$ that does not depend on the future increments of the process. Our asymptotic results are uniform over the whole class of such random times. Particular examples are given by stopping times and by $τ$ independent of the processes. We link our results with random walk theory.

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

Stochastic Processes and their Applications 数学-统计学与概率论

CiteScore

2.90

自引率

7.10%

发文量

180

审稿时长

23.6 weeks

期刊介绍： Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.