{"title":"关于球面双分数布朗运动的注记","authors":"Mohamed El Omari","doi":"10.15559/22-vmsta207","DOIUrl":null,"url":null,"abstract":"The existence of the bifractional Brownian motion ${B_{H,K}}$ indexed by a sphere when $K\\in (-\\infty ,1]\\setminus \\{0\\}$ and $H\\in (0,1/2]$ is discussed, and the asymptotics of its excursion probability $\\mathbb{P}\\left\\{{\\sup _{M\\in \\mathbb{S}}}{B_{H,K}}(M)>x\\right\\}$ as $x\\to \\infty $ is studied.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"2013 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2021-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Notes on spherical bifractional Brownian motion\",\"authors\":\"Mohamed El Omari\",\"doi\":\"10.15559/22-vmsta207\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The existence of the bifractional Brownian motion ${B_{H,K}}$ indexed by a sphere when $K\\\\in (-\\\\infty ,1]\\\\setminus \\\\{0\\\\}$ and $H\\\\in (0,1/2]$ is discussed, and the asymptotics of its excursion probability $\\\\mathbb{P}\\\\left\\\\{{\\\\sup _{M\\\\in \\\\mathbb{S}}}{B_{H,K}}(M)>x\\\\right\\\\}$ as $x\\\\to \\\\infty $ is studied.\",\"PeriodicalId\":42685,\"journal\":{\"name\":\"Modern Stochastics-Theory and Applications\",\"volume\":\"2013 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2021-06-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Modern Stochastics-Theory and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15559/22-vmsta207\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Modern Stochastics-Theory and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15559/22-vmsta207","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
The existence of the bifractional Brownian motion ${B_{H,K}}$ indexed by a sphere when $K\in (-\infty ,1]\setminus \{0\}$ and $H\in (0,1/2]$ is discussed, and the asymptotics of its excursion probability $\mathbb{P}\left\{{\sup _{M\in \mathbb{S}}}{B_{H,K}}(M)>x\right\}$ as $x\to \infty $ is studied.
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