Poisson approximation of Rademacher functionals by the Chen-Stein method and Malliavin calculus
Probability
2017-07-26 v3
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.
Keywords
Cite
@article{arxiv.1505.01417,
title = {Poisson approximation of Rademacher functionals by the Chen-Stein method and Malliavin calculus},
author = {Kai Krokowski},
journal= {arXiv preprint arXiv:1505.01417},
year = {2017}
}
Comments
Comments on version 2: An error in the bound of Theorem 3.4 was corrected. Corollary 3.9, Remark 3.10 and Remark 3.14 were added to discuss some concrete applications to Theorem 3.7 and Theorem 3.13 (formerly Theorem 3.11)