Multivariate Gaussian approximations on Markov chaoses

被引：8

作者：

Campese, Simon ^{[1
]}

Nourdin, Ivan ^{[2
]}

Peccati, Giovanni ^{[2
]}

Poly, Guillaume ^{[3
]}

机构：

[1] Univ Roma Tor Vergata, I-00173 Rome, Italy

[2] Univ Luxembourg, Luxembourg, Luxembourg

[3] Univ Rennes 1, F-35014 Rennes, France

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2016年 / 21卷

关键词：

Markov diffusion generator; Fourth Moment Theorem; multivariate normal approximations; CENTRAL LIMIT-THEOREMS; MULTIPLE; INTEGRALS;

D O I：

10.1214/16-ECP4615

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove a version of the multidimensional Fourth Moment Theorem for chaotic random vectors, in the general context of diffusion Markov generators. In addition to the usual componentwise convergence and unlike the infinite-dimensional Ornstein-Uhlenbeck generator case, another moment-type condition is required to imply joint convergence of of a given sequence of vectors.

引用

页数：9

共 14 条

[1]

[Anonymous], 2012, CAMBRIDGE TRACTS MAT

[2] GENERALIZATION OF THE NUALART-PECCATI CRITERION [J].