Convergence of random oscillatory integrals in the presence of long-range dependence and application to homogenization

in Probability and Mathematical Statistics (2018), 38(2), 271-286

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

in Stochastic Processes and Their Applications (2017), 127(5), 1622-1636

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 ... [more ▼]

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 [less ▲]

A Peccati-Tudor type theorem for Rademacher chaoses

E-print/Working paper (2017)

In this article, we prove that in the Rademacher setting, a random vector with chaotic components is close in distribution to a centred Gaussian vector, if both the maximal influence of the associated ... [more ▼]

In this article, we prove that in the Rademacher setting, a random vector with chaotic components is close in distribution to a centred Gaussian vector, if both the maximal influence of the associated kernel and the fourth cumulant of each component is small. In particular, we recover the univariate case recently established in D\"obler and Krokowski (2017). Our main strategy consists in a novel adaption of the exchangeable pairs couplings initiated in Nourdin and Zheng (2017), as well as its combination with estimates via chaos decomposition. [less ▲]