{"title":"On the Sum of Gaussian Martingale and an Independent Fractional Brownian Motion","authors":"R. Belfadli, M. Chadad, M. Erraoui","doi":"10.1137/s0040585x97t991441","DOIUrl":null,"url":null,"abstract":"In the same context as in the seminal paper [P. Cheridito, Bernoulli, 7 (2001), pp. 913--934], we are concerned with the semimartingale property of the sum of some Gaussian martingale and an independent fractional Brownian motion with Hurst parameter $H \\in (0,1)$. At the same time, we emphasize that the Markov property is lost even if the martingale owns it.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"26 1","pages":"0"},"PeriodicalIF":0.5000,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Probability and its Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/s0040585x97t991441","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
In the same context as in the seminal paper [P. Cheridito, Bernoulli, 7 (2001), pp. 913--934], we are concerned with the semimartingale property of the sum of some Gaussian martingale and an independent fractional Brownian motion with Hurst parameter $H \in (0,1)$. At the same time, we emphasize that the Markov property is lost even if the martingale owns it.
期刊介绍：
Theory of Probability and Its Applications (TVP) accepts original articles and communications on the theory of probability, general problems of mathematical statistics, and applications of the theory of probability to natural science and technology. Articles of the latter type will be accepted only if the mathematical methods applied are essentially new.
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