On lacunary wavelet series

• 成果类型: Article
• 署名作者: Jaffard, S
• 署名单位: Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/aoap/1019737675
• 发表日期: 2000
• 页码: 313-329
• 关键词: chirps

摘要

We prove that the Holder singularities of random lacunary wavelet series are chirps located on random fractal sets. We determine the Hausdorff dimensions of these singularities, and the a.e. modulus of continuity of the series. Lacunary wavelet series thus turn out to be a new example of multifractal functions.