{"title":"On the nth-order subfractional Brownian motion","authors":"E. Mohamed, Mabdaoui Mohamed","doi":"10.15672/hujms.1180888","DOIUrl":null,"url":null,"abstract":"In the present work, we introduce the nth-Order subfractional Brownian motion (S_H^n (t), t ≥ 0) with Hurst index H ∈ (n − 1,n) and order n ≥ 1; then we examine some\nof its basic properties: self-similarity, long-range dependence, non Markovian nature and semimartingale property. A local law of iterated logarithm for S_H^n (t) is also established.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"186 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2023-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Hacettepe Journal of Mathematics and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.15672/hujms.1180888","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In the present work, we introduce the nth-Order subfractional Brownian motion (S_H^n (t), t ≥ 0) with Hurst index H ∈ (n − 1,n) and order n ≥ 1; then we examine some
of its basic properties: self-similarity, long-range dependence, non Markovian nature and semimartingale property. A local law of iterated logarithm for S_H^n (t) is also established.
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Hacettepe Journal of Mathematics and Statistics covers all aspects of Mathematics and Statistics. Papers on the interface between Mathematics and Statistics are particularly welcome, including applications to Physics, Actuarial Sciences, Finance and Economics.
We strongly encourage submissions for Statistics Section including current and important real world examples across a wide range of disciplines. Papers have innovations of statistical methodology are highly welcome. Purely theoretical papers may be considered only if they include popular real world applications.
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