{"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":null,"pages":null},"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}
引用次数: 0
Abstract
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.
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