Wolfgang Bock, Sascha Desmettre, José Luís da Silva
{"title":"Integral representation of generalized grey Brownian motion.","authors":"Wolfgang Bock, Sascha Desmettre, José Luís da Silva","doi":"10.1080/17442508.2019.1641093","DOIUrl":null,"url":null,"abstract":"<p><p>In this paper, we investigate the representation of a class of non-Gaussian processes, namely generalized grey Brownian motion, in terms of a weighted integral of a stochastic process which is a solution of a certain stochastic differential equation. In particular, the underlying process can be seen as a non-Gaussian extension of the Ornstein-Uhlenbeck process, hence generalizing the representation results of Muravlev, Russian Math. Surveys 66 (2), 2011 as well as Harms and Stefanovits, Stochastic Process. Appl. 129, 2019 to the non-Gaussian case.</p>","PeriodicalId":93054,"journal":{"name":"Stochastics (Abingdon, England : 2005)","volume":"92 4","pages":"552-565"},"PeriodicalIF":0.0000,"publicationDate":"2019-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7455069/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastics (Abingdon, England : 2005)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/17442508.2019.1641093","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
In this paper, we investigate the representation of a class of non-Gaussian processes, namely generalized grey Brownian motion, in terms of a weighted integral of a stochastic process which is a solution of a certain stochastic differential equation. In particular, the underlying process can be seen as a non-Gaussian extension of the Ornstein-Uhlenbeck process, hence generalizing the representation results of Muravlev, Russian Math. Surveys 66 (2), 2011 as well as Harms and Stefanovits, Stochastic Process. Appl. 129, 2019 to the non-Gaussian case.
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