{"title":"Generalized Wiener–Hermite integrals and rough non-Gaussian Ornstein–Uhlenbeck process","authors":"Obayda Assaad, Charles-Philippe Diez, C. Tudor","doi":"10.1080/17442508.2022.2068955","DOIUrl":null,"url":null,"abstract":"We discuss several properties of the generalized Hermite process, which is a non-Gaussian self-similar processes with self-similarity index belonging to the whole interval . We also define Wiener integral with respect to this process and as an application, we define and study its associated Ornstein–Uhlenbeck process.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"1 1","pages":"191 - 210"},"PeriodicalIF":1.1000,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Finance and Stochastics","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1080/17442508.2022.2068955","RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
引用次数: 2
Abstract
We discuss several properties of the generalized Hermite process, which is a non-Gaussian self-similar processes with self-similarity index belonging to the whole interval . We also define Wiener integral with respect to this process and as an application, we define and study its associated Ornstein–Uhlenbeck process.
期刊介绍：
The purpose of Finance and Stochastics is to provide a high standard publication forum for research
- in all areas of finance based on stochastic methods
- on specific topics in mathematics (in particular probability theory, statistics and stochastic analysis) motivated by the analysis of problems in finance.
Finance and Stochastics encompasses - but is not limited to - the following fields:
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- statistical and empirical financial studies based on advanced stochastic methods
- numerical and stochastic solution techniques for problems in finance
- intertemporal economics, uncertainty and information in relation to finance.
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