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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:127

Article

Zheng, Guangqu¹ 

[1] Univ Luxembourg, URM, 6 Rue Richard Coudenhove Kalergi, L-1359 Luxembourg, Luxembourg

关键词: Rademacher functional;    Normal approximation;    Wasserstein distance;    Almost sure central limit theorem;    Malliavin-Stein approach;   

DOI  :  10.1016/j.spa.2016.09.002

来源: Elsevier

【 摘 要 】

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 et al. (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. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free