{"title":"推广Karhunen - loeve du pont brownien的发展","authors":"Jean-Renaud Pycke","doi":"10.1016/S0764-4442(01)02053-5","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we give the Karhunen–Loève expansion of a centered Gaussian process whose covariance function depends on two parameters, including the covariance function of the Brownian bridge as a special case. A statistical application, related to the weighted uniform empirical process is provided.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 685-688"},"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)02053-5","citationCount":"6","resultStr":"{\"title\":\"Une généralisation du développement de Karhunen–Loève du pont brownien\",\"authors\":\"Jean-Renaud Pycke\",\"doi\":\"10.1016/S0764-4442(01)02053-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper we give the Karhunen–Loève expansion of a centered Gaussian process whose covariance function depends on two parameters, including the covariance function of the Brownian bridge as a special case. A statistical application, related to the weighted uniform empirical process is provided.</p></div>\",\"PeriodicalId\":100300,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"volume\":\"333 7\",\"pages\":\"Pages 685-688\"},\"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)02053-5\",\"citationCount\":\"6\",\"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/S0764444201020535\",\"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/S0764444201020535","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Une généralisation du développement de Karhunen–Loève du pont brownien
In this paper we give the Karhunen–Loève expansion of a centered Gaussian process whose covariance function depends on two parameters, including the covariance function of the Brownian bridge as a special case. A statistical application, related to the weighted uniform empirical process is provided.