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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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.

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

First available in Project Euclid: 17 August 2010

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

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


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.

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