{"title":"高斯鞅与独立分数布朗运动的和","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":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":null,\"pages\":null},\"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}","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
摘要
在与开创性论文相同的上下文中[P。Cheridito, Bernoulli, 7 (2001)， pp. 913—934]，我们关注具有Hurst参数$H \in(0,1)$的高斯鞅和独立分数布朗运动的和的半鞅性质。同时，我们强调即使鞅拥有马尔可夫属性，马尔可夫属性也会丢失。
On the Sum of Gaussian Martingale and an Independent Fractional Brownian Motion
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.
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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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