Poisson approximation of Rademacher functionals by the Chen-Stein method and Malliavin calculus

2015/05/06 by Kai Krokowski, Krokowski, Kai
Economics, Econometrics and Finance · Mathematics · #60F05 #60G57 #60H07 #Advanced Banach Space Theory #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1505.01417

openalex publication_date 2015/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

New bounds on the total variation distance between the law of integer valued functionals of possibly non-symmetric and non-homogeneous infinite Rademacher sequences and the Poisson distribution are established. They are based on a combination of the Chen-Stein method and a discrete version of Malliavin calculus. We give some applications to shifted discrete multiple stochastic integrals.

Related

• The Chen-Stein method for Poisson functionals
• Stein's method and stochastic analysis of Rademacher functionals
• Improved Lower Bounds on the Total Variation Distance for the Poisson Approximation
• Stein's method and normal approximation of Poisson functionals
• Poisson and normal approximations for the measurable functions of independent random variables