# A pure jump Markov process with a random singularity spectrum - Mathematics > Probability

A pure jump Markov process with a random singularity spectrum - Mathematics > Probability - Download this document for free, or read online. Document in PDF available to download.

Abstract: We construct a non-decreasing pure jump Markov process, whose jump measureheavily depends on the values taken by the process. We determine thesingularity spectrum of this process, which turns out to be random and todepend locally on the values taken by the process. The result relies on fineproperties of the distribution of Poisson point processes and on ubiquitytheorems.

Author: ** Julien Barral, Nicolas Fournier, Stephane Jaffard, Stephane Seuret**

Source: https://arxiv.org/