节制时空分数负二项过程

arXiv - MATH - Probability Pub Date : 2024-09-11 DOI:arxiv-2409.07044

Shilpa, Ashok Kumar Pathak, Aditya Maheshwari

{"title":"节制时空分数负二项过程","authors":"Shilpa, Ashok Kumar Pathak, Aditya Maheshwari","doi":"arxiv-2409.07044","DOIUrl":null,"url":null,"abstract":"In this paper, we define a tempered space-time fractional negative binomial\nprocess (TSTFNBP) by subordinating the fractional Poisson process with an\nindependent tempered Mittag-Leffler L\\'{e}vy subordinator. We study its\ndistributional properties and its connection to partial differential equations.\nWe derive the asymptotic behavior of its fractional order moments and\nlong-range dependence property. It is shown that the TSTFNBP exhibits\noverdispersion. We also obtain some results related to the first-passage time.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Tempered space-time fractional negative binomial process\",\"authors\":\"Shilpa, Ashok Kumar Pathak, Aditya Maheshwari\",\"doi\":\"arxiv-2409.07044\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we define a tempered space-time fractional negative binomial\\nprocess (TSTFNBP) by subordinating the fractional Poisson process with an\\nindependent tempered Mittag-Leffler L\\\\'{e}vy subordinator. We study its\\ndistributional properties and its connection to partial differential equations.\\nWe derive the asymptotic behavior of its fractional order moments and\\nlong-range dependence property. It is shown that the TSTFNBP exhibits\\noverdispersion. We also obtain some results related to the first-passage time.\",\"PeriodicalId\":501245,\"journal\":{\"name\":\"arXiv - MATH - Probability\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Probability\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.07044\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.07044","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

本文通过将分数泊松过程与独立的回火米塔格-勒夫勒 L\'{e}vy 附属器进行附属，定义了回火时空分数负二项式过程（TSTFNBP）。我们研究了它的分布特性及其与偏微分方程的联系，并推导出其分数阶矩的渐近行为和长程依赖特性。结果表明，TSTFNBP 表现出过度离散性。我们还得到了一些与首过时间相关的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Tempered space-time fractional negative binomial process

In this paper, we define a tempered space-time fractional negative binomial process (TSTFNBP) by subordinating the fractional Poisson process with an independent tempered Mittag-Leffler L\'{e}vy subordinator. We study its distributional properties and its connection to partial differential equations. We derive the asymptotic behavior of its fractional order moments and long-range dependence property. It is shown that the TSTFNBP exhibits overdispersion. We also obtain some results related to the first-passage time.

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

arXiv - MATH - Probability

自引率

0.00%

发文量