A pure jump Markov process with a random singularity spectrum
Julien Barral, Nicolas Fournier, Stéphane Jaffard, and Stéphane Seuret
Source: Ann. Probab. Volume 38, Number 5
(2010), 1924-1946.
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.
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Keywords: Singularity spectrum; Hausdorff dimension; Markov processes; jump processes; stochastic differential equations; Poisson measures
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Permanent link to this document: http://projecteuclid.org/euclid.aop/1282053776
Digital Object Identifier: doi:10.1214/10-AOP533
Zentralblatt MATH identifier: 05793426
Mathematical Reviews number (MathSciNet): MR2722790
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