English

Normal approximation and almost sure central limit theorem for non-symmetric Rademacher functionals

Probability 2018-10-16 v2

Abstract

In this work, we study the normal approximation and almost sure central limit theorems for some functionals of an independent sequence of Rademacher random variables. In particular, we provide a new chain rule that improves the one derived by Nourdin, Peccati and Reinert(2010) and then we deduce the bound on Wasserstein distance for normal approximation using the (discrete) Malliavin-Stein approach. Besides, we are able to give the almost sure central limit theorem for a sequence of random variables inside a fixed Rademacher chaos using the Ibragimov-Lifshits criterion.

Keywords

Cite

@article{arxiv.1603.04661,
  title  = {Normal approximation and almost sure central limit theorem for non-symmetric Rademacher functionals},
  author = {Guangqu Zheng},
  journal= {arXiv preprint arXiv:1603.04661},
  year   = {2018}
}

Comments

restructured, revised, submitted

R2 v1 2026-06-22T13:11:16.625Z