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

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  • Zheng, Guangqu

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 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.

Suggested Citation

  • Zheng, Guangqu, 2017. "Normal approximation and almost sure central limit theorem for non-symmetric Rademacher functionals," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1622-1636.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:5:p:1622-1636
    DOI: 10.1016/j.spa.2016.09.002
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    References listed on IDEAS

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    1. Bercu, Bernard & Nourdin, Ivan & Taqqu, Murad S., 2010. "Almost sure central limit theorems on the Wiener space," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1607-1628, August.
    2. Lacey, Michael T. & Philipp, Walter, 1990. "A note on the almost sure central limit theorem," Statistics & Probability Letters, Elsevier, vol. 9(3), pages 201-205, March.
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    Cited by:

    1. Jing Zhang & Lixia Zhang & Caishi Wang, 2022. "Probabilistic Interpretation of Number Operator Acting on Bernoulli Functionals," Mathematics, MDPI, vol. 10(15), pages 1-11, July.

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