{"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}
引用次数: 2
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.
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