Malliavin-Stein method for multi-dimensional U-statistics of Poisson point processes

2011/11/09 by Minh, Nguyen Tuan
#60F05 #60G55 #60H07 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1111.2140

Abstract

In this paper, we give an upper bound for a probabilistic distance between a Gaussian vector and a vector of U-statistics of Poisson point processes by applying Malliavin-Stein inequality on the Poisson space.

Related

• Multivariate Poisson and Poisson process approximations with applications to Bernoulli sums and U-statistics
• Normal approximation of Poisson functionals in Kolmogorov distance
• Multi-dimensional Gaussian fluctuations on the Poisson space
• The Stein-Dirichlet-Malliavin method
• Stein's method and Papangelou intensity for Poisson or Cox process approximation