A PURE JUMP MARKOV PROCESS WITH A RANDOM SINGULARITY SPECTRUM

• 成果类型: Article
• 署名作者: Barral, Julien; Fournier, Nicolas; Jaffard, Stephane; Seuret, Stephane
• 署名单位: Universite Paris 13; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP533
• 发表日期: 2010
• 页码: 1924-1946
• 关键词: multifractal nature; Hausdorff Dimension; wavelet series; Levy processes

摘要

We construct a nondecreasing pure jump Markov process, whose jump measure heavily depends on the values taken by the process. We determine the singularity spectrum of this process, which turns out to be random and to depend locally on the values taken by the process. The result relies on fine properties of the distribution of Poisson point processes and on ubiquity theorems.