Malliavin and Dirichlet structures for independent random variables

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Decreusefond, Laurent¹  Halconruy, Helene^1,2 

[1] Univ Paris Saclay, Telecom ParisTech, LTCI, F-75013 Paris, France

[2] ESME Sudria, F-75015 Paris, France

关键词: Dirichlet structure;    Ewens distribution;    Log-Sobolev inequality;    Malliavin calculus;    Stein's method;    Talagrand inequality;   

DOI  :  10.1016/j.spa.2018.07.019

来源: Elsevier

【 摘 要 】

On any denumerable product of probability spaces, we construct a Malliavin gradient and then a divergence and a number operator. This yields a Dirichlet structure which can be shown to approach the usual structures for Poisson and Brownian processes. We obtain versions of almost all the classical functional inequalities in discrete settings which show that the Efron-Stein inequality can be interpreted as a Poincare inequality or that the Hoeffding decomposition of U-statistics can be interpreted as an avatar of the Clark representation formula. Thanks to our framework, we obtain a bound for the distance between the distribution of any functional of independent variables and the Gaussian and Gamma distributions. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free