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2014 Portmanteau inequalities on the Poisson space: mixed regimes and multidimensional clustering
Solesne Bourguin, Giovanni Peccati
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Electron. J. Probab. 19: 1-42 (2014). DOI: 10.1214/EJP.v19-2879

Abstract

Using Malliavin operators together with an interpolation technique inspired by Arratia, Goldstein and Gordon (1989), we prove a new inequality on the Poisson space, allowing one to measure the distance between the laws of a general random vector, and of a target random element composed of Gaussian and Poisson random variables. Several consequences are deduced from this result, in particular: (1) new abstract criteria for multidimensional stable convergence on the Poisson space, (2) a class of mixed limit theorems, involving both Poisson and Gaussian limits, (3) criteria for the asymptotic independence of U-statistics following Gaussian and Poisson asymptotic regimes. Our results generalize and unify several previous findings in the field. We provide an application to joint sub-graph counting in random geometric graphs.

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Solesne Bourguin. Giovanni Peccati. "Portmanteau inequalities on the Poisson space: mixed regimes and multidimensional clustering." Electron. J. Probab. 19 1 - 42, 2014. https://doi.org/10.1214/EJP.v19-2879

Information

Accepted: 11 August 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1316.60089
MathSciNet: MR3248195
Digital Object Identifier: 10.1214/EJP.v19-2879

Subjects:
Primary: 60H07
Secondary: 60D05 , 60F05 , 60G55

Keywords: Chen-Stein method , contractions , Malliavin calculus , Poisson Limit Theorems , Poisson Space , Random graphs , total variation distance , Wiener Chaos

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