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September 2010 A pure jump Markov process with a random singularity spectrum
Julien Barral, Nicolas Fournier, Stéphane Jaffard, Stéphane Seuret
Ann. Probab. 38(5): 1924-1946 (September 2010). DOI: 10.1214/10-AOP533


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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Julien Barral. Nicolas Fournier. Stéphane Jaffard. Stéphane Seuret. "A pure jump Markov process with a random singularity spectrum." Ann. Probab. 38 (5) 1924 - 1946, September 2010.


Published: September 2010
First available in Project Euclid: 17 August 2010

zbMATH: 1205.60148
MathSciNet: MR2722790
Digital Object Identifier: 10.1214/10-AOP533

Primary: 28A78 , 28A80 , 60J75

Keywords: Hausdorff dimension , Jump processes , Markov processes , Poisson measures , Singularity spectrum , Stochastic differential equations

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 5 • September 2010
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