An improved bound for the Gaussian concentration inequality

In this note, we provide an improved bound for the Gaussian concentration inequality. Our proof is short and bases on the integration-by-parts formula for the gaussian measure.Comment: 4 page

Gaussian lower bounds for the density via Malliavin calculus

In this paper, based on a known formula, we use a simple idea to get a new representation for the density of Malliavin differentiable random variables. This new representation is particularly useful for finding lower bounds for the density.Comment: To appear in Comptes Rendus Mathematique, 10 page

“Living” Epics in Central Highland-Vietnam

This article is about h’mon, an epic genre of Bahnar ethnic in the Central Highlands of Vietnam. Typical of this epic type is H’mon Dam Giong (or The Dam Giong epics). The contents of this article include space and mode of performance of h’mon; characteristics of the “living epic” of h’mon (It is the ability to refresh the content of h’mon by adding new details); characteristics of the character system (including the central character and the re-appearing characters)

Rates of Fisher information convergence in the central limit theorem for nonlinear statistics

We develop a general method to study the Fisher information distance in central limit theorem for nonlinear statistics. We first construct explicit representations for the score functions. We then use these representations to derive quantitative estimates for the Fisher information distance. To illustrate the applicability of our approach, explicit rates of Fisher information convergence for quadratic forms and the functions of sample means are provided. The case of the sums of independent random variables are discussed as well.Comment: 35 pages. Added Example 3.1, Corollary 4.1, Corollary 4.3 and Subsection 4.

Some new concentration inequalities for the It\^o stochastic integral

In this paper, based on the techniques of Malliavin calculus, we provide some new concentration inequalities for the running supremum of It\^o stochastic integral with unbounded integrands. Several applications and examples are provided as well.Comment: 17 page