A PURE JUMP MARKOV PROCESS WITH A RANDOM SINGULARITY SPECTRUM

被引：17

作者：

Barral, Julien ^{[1
]}

Fournier, Nicolas ^{[2
]}

Jaffard, Stephane ^{[2
]}

Seuret, Stephane ^{[2
]}

机构：

[1] Univ Paris 13, Inst Galilee, F-93430 Villetaneuse, France

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

来源：

ANNALS OF PROBABILITY | 2010年 / 38卷 / 05期

关键词：

Singularity spectrum; Hausdorff dimension; Markov processes; jump processes; stochastic differential equations; Poisson measures; MULTIFRACTAL NATURE; HAUSDORFF DIMENSION; WAVELET SERIES; LEVY PROCESSES;

D O I：

10.1214/10-AOP533

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 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.

引用

页码：1924 / 1946

页数：23

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