Stein-Malliavin method for discrete alpha stable point processes (workshop ERC Nemo Processus ponctuels et graphes aléatoires unimodulaires)
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The notion of discrete alpha-stable point processes generalizes to point processes the notion of stable distribution. It has been introduced and studied by Davydov, Molchanov and Zuyev a few years ago. Their stability property leaves a large degree of variability in the choice of their driving characteristics but enforces a rich mathematical structure. We show how to build a Dirichlet-Malliavin structure for these processes and we apply this framework to several limit theorems. Some known results for Poisson point processes appear as corollaries of the present theorems.
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