Slow, ordinary and rapid points for Gaussian Wavelets Series and application to Fractional Brownian Motions

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2022-03-10 DOI:10.30757/alea.v19-59

C. Esser, L. Loosveldt

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.

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高斯小波级数的慢、常、快点及其在分数布朗运动中的应用

.我们研究了高斯小波级数的Hölder正则性，并表明它们几乎可以肯定地显示出三种类型的点：慢点、普通点和快速点。特别地，这个事实适用于分数布朗运动。最后，我们注意到慢点的存在对于这些函数是特殊的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Alea-Latin American Journal of Probability and Mathematical Statistics STATISTICS & PROBABILITY-

CiteScore

1.10

自引率

0.00%

发文量

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.