{"title":"k阶从属复合泊松过程","authors":"A. Sengar, N. S. Upadhye","doi":"10.15559/20-vmsta165","DOIUrl":null,"url":null,"abstract":"In this article, the compound Poisson processes of order $k$ (CPPoK) is introduced and its properties are discussed. Further, using mixture of tempered stable subordinator (MTSS) and its right continuous inverse, the two subordinated CPPoK with various distributional properties are studied. It is also shown that space and tempered space fractional versions of CPPoK and PPoK can be obtained, which generalize the results in the literature.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"16 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Subordinated compound Poisson processes of order k\",\"authors\":\"A. Sengar, N. S. Upadhye\",\"doi\":\"10.15559/20-vmsta165\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, the compound Poisson processes of order $k$ (CPPoK) is introduced and its properties are discussed. Further, using mixture of tempered stable subordinator (MTSS) and its right continuous inverse, the two subordinated CPPoK with various distributional properties are studied. It is also shown that space and tempered space fractional versions of CPPoK and PPoK can be obtained, which generalize the results in the literature.\",\"PeriodicalId\":42685,\"journal\":{\"name\":\"Modern Stochastics-Theory and Applications\",\"volume\":\"16 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2020-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Modern Stochastics-Theory and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15559/20-vmsta165\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Modern Stochastics-Theory and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15559/20-vmsta165","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Subordinated compound Poisson processes of order k
In this article, the compound Poisson processes of order $k$ (CPPoK) is introduced and its properties are discussed. Further, using mixture of tempered stable subordinator (MTSS) and its right continuous inverse, the two subordinated CPPoK with various distributional properties are studied. It is also shown that space and tempered space fractional versions of CPPoK and PPoK can be obtained, which generalize the results in the literature.
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