The Annals of Probability

A pure jump Markov process with a random singularity spectrum

Julien Barral, Nicolas Fournier, Stéphane Jaffard, and Stéphane Seuret

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Abstract

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.

Article information

Source
Ann. Probab., Volume 38, Number 5 (2010), 1924-1946.

Dates
First available in Project Euclid: 17 August 2010

Permanent link to this document
https://projecteuclid.org/euclid.aop/1282053776

Digital Object Identifier
doi:10.1214/10-AOP533

Mathematical Reviews number (MathSciNet)
MR2722790

Zentralblatt MATH identifier
1205.60148

Subjects
Primary: 60J75: Jump processes 28A78: Hausdorff and packing measures 28A80: Fractals [See also 37Fxx]

Keywords
Singularity spectrum Hausdorff dimension Markov processes jump processes stochastic differential equations Poisson measures

Citation

Barral, Julien; Fournier, Nicolas; Jaffard, Stéphane; Seuret, Stéphane. A pure jump Markov process with a random singularity spectrum. Ann. Probab. 38 (2010), no. 5, 1924--1946. doi:10.1214/10-AOP533. https://projecteuclid.org/euclid.aop/1282053776


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