离散时霍克斯过程及其补偿器研究

Pub Date : 2024-06-25 DOI:10.1016/j.spl.2024.110192

Utpal Jyoti Deba Sarma, Dharmaraja Selvamuthu

{"title":"离散时霍克斯过程及其补偿器研究","authors":"Utpal Jyoti Deba Sarma, Dharmaraja Selvamuthu","doi":"10.1016/j.spl.2024.110192","DOIUrl":null,"url":null,"abstract":"<div><p>The discrete-time Hawkes process (DTHP) is a sub-class of <span><math><mi>g</mi></math></span>-functions that serves as a discrete-time version of the continuous-time Hawkes process (CTHP). Like the CTHP, the DTHP also has the self-exciting property and its intensity depends on the entire history. In this paper, we study the asymptotic behavior of the DTHP and its compensator. We further analyze the moment generating function (MGF) of the DTHP and obtain some bounds and convergence results on the scaled logarithmic MGF of the DTHP.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Study of discrete-time Hawkes process and its compensator\",\"authors\":\"Utpal Jyoti Deba Sarma, Dharmaraja Selvamuthu\",\"doi\":\"10.1016/j.spl.2024.110192\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The discrete-time Hawkes process (DTHP) is a sub-class of <span><math><mi>g</mi></math></span>-functions that serves as a discrete-time version of the continuous-time Hawkes process (CTHP). Like the CTHP, the DTHP also has the self-exciting property and its intensity depends on the entire history. In this paper, we study the asymptotic behavior of the DTHP and its compensator. We further analyze the moment generating function (MGF) of the DTHP and obtain some bounds and convergence results on the scaled logarithmic MGF of the DTHP.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167715224001615\",\"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://www.sciencedirect.com/science/article/pii/S0167715224001615","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

离散时间霍克斯过程（DTHP）是 g 函数的一个子类，是连续时间霍克斯过程（CTHP）的离散时间版本。与 CTHP 一样，DTHP 也具有自激特性，其强度取决于整个历史。本文研究了 DTHP 及其补偿器的渐近行为。我们进一步分析了 DTHP 的矩生成函数 (MGF)，并得到了 DTHP 的缩放对数 MGF 的一些边界和收敛结果。

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

微信好友朋友圈 QQ好友复制链接

Study of discrete-time Hawkes process and its compensator

The discrete-time Hawkes process (DTHP) is a sub-class of $g$ -functions that serves as a discrete-time version of the continuous-time Hawkes process (CTHP). Like the CTHP, the DTHP also has the self-exciting property and its intensity depends on the entire history. In this paper, we study the asymptotic behavior of the DTHP and its compensator. We further analyze the moment generating function (MGF) of the DTHP and obtain some bounds and convergence results on the scaled logarithmic MGF of the DTHP.

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