{"title":"Slow, ordinary and rapid points for Gaussian Wavelets Series and application to Fractional Brownian Motions","authors":"C. Esser, L. Loosveldt","doi":"10.30757/alea.v19-59","DOIUrl":null,"url":null,"abstract":". We study the Hölderian regularity of Gaussian wavelets series and show that they dis-play, almost surely, three types of points: slow, ordinary and rapid. In particular, this fact holds for the Fractional Brownian Motion. Finally, we remark that the existence of slow points is specific to these functions.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2022-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Alea-Latin American Journal of Probability and Mathematical Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.30757/alea.v19-59","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: 7
Abstract
. We study the Hölderian regularity of Gaussian wavelets series and show that they dis-play, almost surely, three types of points: slow, ordinary and rapid. In particular, this fact holds for the Fractional Brownian Motion. Finally, we remark that the existence of slow points is specific to these functions.
期刊介绍：
ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted.
ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper.
ALEA is affiliated with the Institute of Mathematical Statistics.
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