文章基本信息

标题：Optimal Convergence Rates and One-Term Edgeworth Expansions for Multidimensional Functionals of Gaussian Fields
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作者：Simon Campese
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2013
卷号：X
期号：2
页码：881-919
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We develop techniques for determining the exact asymptotic speed ofconvergence in the multidimensional normal approximation of smooth functions ofGaussian fields. As a by-product, our findings yield exact limits and often give riseto one-term generalized Edgeworth expansions increasing the speed of convergence.Our main mathematical tools are Malliavin calculus, Stein’s method and the FourthMoment Theorem. This work can be seen as an extension of the results of Nourdinand Peccati (2009a) to the multi-dimensional case, with the notable difference thatin our framework covariances are allowed to fluctuate. We apply our findings toexploding functionals of Brownian sheets, vectors of Toeplitz quadratic functionalsand the Breuer-Major Theorem.
关键词：Malliavin calculus; Stein’s method; Gaussian approximation; Edgeworth;expansion; optimality; multiple integral; contraction.