{"title":"随机分布，随机仿射系统，更新过程的抽样","authors":"Christian Mazza, Didier Piau","doi":"10.1016/S0764-4442(01)02120-6","DOIUrl":null,"url":null,"abstract":"<div><p>Let <em>F</em> be a neutral to the right, random distribution function on [0,+∞[, with a stationary subordinator. We introduce new linear functionals of the increments of <em>F</em>. Each of them is distributed like the unique fixed point of a random affine system. For gamma subordinators, we prove, building on earlier work, that their densities involve linear combinations of hypergeometric functions. We apply these ideas to the random sampling of alternating renewal processes.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 669-672"},"PeriodicalIF":0.0000,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02120-6","citationCount":"1","resultStr":"{\"title\":\"Random distributions, random affine systems, sampling of renewal processes\",\"authors\":\"Christian Mazza, Didier Piau\",\"doi\":\"10.1016/S0764-4442(01)02120-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <em>F</em> be a neutral to the right, random distribution function on [0,+∞[, with a stationary subordinator. We introduce new linear functionals of the increments of <em>F</em>. Each of them is distributed like the unique fixed point of a random affine system. For gamma subordinators, we prove, building on earlier work, that their densities involve linear combinations of hypergeometric functions. We apply these ideas to the random sampling of alternating renewal processes.</p></div>\",\"PeriodicalId\":100300,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"volume\":\"333 7\",\"pages\":\"Pages 669-672\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02120-6\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0764444201021206\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0764444201021206","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Random distributions, random affine systems, sampling of renewal processes
Let F be a neutral to the right, random distribution function on [0,+∞[, with a stationary subordinator. We introduce new linear functionals of the increments of F. Each of them is distributed like the unique fixed point of a random affine system. For gamma subordinators, we prove, building on earlier work, that their densities involve linear combinations of hypergeometric functions. We apply these ideas to the random sampling of alternating renewal processes.
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