Normal approximation and almost sure central limit theorem for non-symmetric Rademacher functionals
arXiv:1603.04661 · doi:10.1016/j.spa.2016.09.002
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.
restructured, revised, submitted
References in corpus (5)
- Central limit theorems for sequences of multiple stochastic integrals
- A new method of normal approximation
- Discrete Malliavin-Stein method: Berry-Esseen bounds for random graphs and percolation
- Poisson approximation of Rademacher functionals by the Chen-Stein method and Malliavin calculus
- Berry-Esseen bounds and multivariate limit theorems for functionals of Rademacher sequences
Cited by in corpus (9)
- Fourth moment theorems on the Poisson space in any dimension
- A Peccati-Tudor type theorem for Rademacher chaoses
- A simplified second-order Gaussian Poincaré inequality in discrete setting with applications
- On the fourth moment condition for Rademacher chaos
- Poisson and normal approximations for the measurable functions of independent random variables
- Almost sure central limit theorem for the hyperbolic Anderson model with Lévy white noise
- Malliavin calculus for marked binomial processes: portfolio optimisation in the trinomial model and compound Poisson approximation
- Almost sure central limit theorems for parabolic/hyperbolic Anderson models with Gaussian colored noises
- Spectral Integrals of Bernoulli Generalized Functionals