Multifractal analysis of L,vy fields

被引：16

作者：

Durand, Arnaud ^{[1
]}

Jaffard, Stephane ^{[2
]}

机构：

[1] Univ Paris 11, Math Lab, UMR 8628, F-91405 Orsay, France

[2] Univ Paris Est Creteil Val de Marne UMR 8050, Lab Anal & Math Appl, F-94010 Creteil, France

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2012年 / 153卷 / 1-2期

关键词：

Levy random fields; Multifractal analysis; Hausdorff measures and dimension; Sets with large intersection; Diophantine approximation; Ubiquity; LARGE INTERSECTION; SETS;

D O I：

10.1007/s00440-011-0340-0

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study the pointwise regularity properties of the L,vy fields introduced by T. Mori; these fields are the most natural generalization of L,vy processes to the multivariate setting. We determine their spectrum of singularities, and we show that their Holder singularity sets satisfy a large intersection property in the sense of K. Falconer.

引用

页码：45 / 96

页数：52

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