Normal approximations for wavelet coefficients on spherical Poisson fields

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:409

Article

Durastanti, Claudio¹  Marinucci, Domenico¹  Peccati, Giovanni² 

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

[2] Luxembourg Univ, Unite Rech Math, Luxembourg, Luxembourg

关键词: Berry-Esseen bounds;    Malliavin calculus;    Multidimensional normal approximation;    Poisson process;    Stein's method;    Spherical wavelets;   

DOI  :  10.1016/j.jmaa.2013.06.028

来源: Elsevier

【 摘 要 】

We compute explicit upper bounds on the distance between the law of a multivariate Gaussian distribution and the joint law of wavelet/needlet coefficients based on a homogeneous spherical Poisson field. In particular, we develop some results from Peccati and Zheng (2010) [42], based on Malliavin calculus and Stein's methods, to assess the rate of convergence to Gaussianity for a triangular array of needlet coefficients with growing dimensions. Our results are motivated by astrophysical and cosmological applications, in particular related to the search for point sources in Cosmic Rays data. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free