A pure jump Markov process with a random singularity spectrum
Barral, Julien ; Fournier, Nicolas ; Jaffard, Stéphane ; Seuret, Stéphane
Ann. Probab., Tome 38 (2010) no. 1, p. 1924-1946 / Harvested from Project Euclid
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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.
Publié le : 2010-09-15
Classification:  Singularity spectrum,  Hausdorff dimension,  Markov processes,  jump processes,  stochastic differential equations,  Poisson measures,  60J75,  28A78,  28A80 
@article{1282053776,
     author = {Barral, Julien and Fournier, Nicolas and Jaffard, St\'ephane and Seuret, St\'ephane},
     title = {A pure jump Markov process with a random singularity spectrum},
     journal = {Ann. Probab.},
     volume = {38},
     number = {1},
     year = {2010},
     pages = { 1924-1946},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1282053776}
}

Barral, Julien; Fournier, Nicolas; Jaffard, Stéphane; Seuret, Stéphane. A pure jump Markov process with a random singularity spectrum. Ann. Probab., Tome 38 (2010) no. 1, pp.  1924-1946. http://gdmltest.u-ga.fr/item/1282053776/