Multifractal analysis of L,vy fields

作者：Durand Arnaud^*; Jaffard Stephane

来源：Probability Theory and Related Fields, 2012, 153(1-2): 45-96.

DOI：10.1007/s00440-011-0340-0

• Levy random fields
• Multifractal analysis
• Hausdorff measures and dimension
• Sets with large intersection
• Diophantine approximation
• Ubiquity

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.

• 出版日期2012-6