On the dependence structure of wavelet coefficients for spherical random fields

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Lan, Xiaohong^1,2  Marinucci, Domenico¹ 

[1] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy

[2] Chinese Acad Sci, Inst Math, Beijing 100864, Peoples R China

关键词: Spherical random fields;    Wavelets;    Mexican needlets;    High frequency asymptotics;    Cosmic microwave background radiation;   

DOI  :  10.1016/j.spa.2009.07.005

来源: Elsevier

【 摘 要 】

We consider the correlation structure of the random coefficients for a class of wavelet systems on the sphere (labelled Mexican needlets) which was recently introduced in the literature by [D. Geller, A. Mayeli, Nearly tight frames and space-frequency analysis on compact manifolds, Preprint, 2007. arxiv:0706.3642v2]. We provide necessary and sufficient conditions for these coefficients to be asymptotically uncorrelated in the real and in the frequency domain. Here, the asymptotic theory is developed in the high frequency sense. Statistical applications are also discussed, in particular with reference to the analysis of cosmological data. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free