{"title":"广义Hermite过程(gHp)的Wiener积分。应用范围:具有高频噪声的SDEs","authors":"Atef Lechiheb","doi":"10.1515/rose-2023-2001","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we introduce Wiener integrals with respect to the generalized Hermite process and we prove a non-central limit theorem in which this integral appears as limit. As an application, we investigate the corresponding stochastic differential equations with the generalized Hermite process as a driving noise, we prove the existence and the uniqueness of the solution, and we give a generalization of the Hermite Ornstein–Uhlenbeck process and the Hermite-driving Vasicek process.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"31 1","pages":"87 - 102"},"PeriodicalIF":0.3000,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Wiener integrals with respect to the generalized Hermite process (gHp). Applications: SDEs with gHp noise\",\"authors\":\"Atef Lechiheb\",\"doi\":\"10.1515/rose-2023-2001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this paper, we introduce Wiener integrals with respect to the generalized Hermite process and we prove a non-central limit theorem in which this integral appears as limit. As an application, we investigate the corresponding stochastic differential equations with the generalized Hermite process as a driving noise, we prove the existence and the uniqueness of the solution, and we give a generalization of the Hermite Ornstein–Uhlenbeck process and the Hermite-driving Vasicek process.\",\"PeriodicalId\":43421,\"journal\":{\"name\":\"Random Operators and Stochastic Equations\",\"volume\":\"31 1\",\"pages\":\"87 - 102\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Random Operators and Stochastic Equations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/rose-2023-2001\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Operators and Stochastic Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/rose-2023-2001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Wiener integrals with respect to the generalized Hermite process (gHp). Applications: SDEs with gHp noise
Abstract In this paper, we introduce Wiener integrals with respect to the generalized Hermite process and we prove a non-central limit theorem in which this integral appears as limit. As an application, we investigate the corresponding stochastic differential equations with the generalized Hermite process as a driving noise, we prove the existence and the uniqueness of the solution, and we give a generalization of the Hermite Ornstein–Uhlenbeck process and the Hermite-driving Vasicek process.