{"title":"带赫斯特指数0H1/2的分数阶布朗运动到包含任意正指数幂积分的高斯鞅子空间的距离","authors":"O. Banna, Filipp Buryak, Y. Mishura","doi":"10.15559/20-VMSTA156","DOIUrl":null,"url":null,"abstract":"We find the best approximation of the fractional Brownian motion with the Hurst index $H\\in (0,1/2)$ by Gaussian martingales of the form $\\int _0^ts^{\\gamma}dW_s$, where $W$ is a Wiener process, $\\gamma >0$.","PeriodicalId":8470,"journal":{"name":"arXiv: Probability","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Distance from fractional Brownian motion with associated Hurst index 0<</mo>H<</mo>1/2 to the subspaces of Gaussian martingales involving power integrands with an arbitrary positive exponent\",\"authors\":\"O. Banna, Filipp Buryak, Y. Mishura\",\"doi\":\"10.15559/20-VMSTA156\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We find the best approximation of the fractional Brownian motion with the Hurst index $H\\\\in (0,1/2)$ by Gaussian martingales of the form $\\\\int _0^ts^{\\\\gamma}dW_s$, where $W$ is a Wiener process, $\\\\gamma >0$.\",\"PeriodicalId\":8470,\"journal\":{\"name\":\"arXiv: Probability\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-06-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Probability\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15559/20-VMSTA156\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15559/20-VMSTA156","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Distance from fractional Brownian motion with associated Hurst index 0<H<1/2 to the subspaces of Gaussian martingales involving power integrands with an arbitrary positive exponent
We find the best approximation of the fractional Brownian motion with the Hurst index $H\in (0,1/2)$ by Gaussian martingales of the form $\int _0^ts^{\gamma}dW_s$, where $W$ is a Wiener process, $\gamma >0$.
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