On the rate of convergence to Rosenblatt-type distribution

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:425

Article

Anh, Vo¹  Leonenko, Nikolai²  Olenko, Andriy³ 

[1] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia

[2] Cardiff Univ, Sch Math, Cardiff CF24 4AG, S Glam, Wales

[3] La Trobe Univ, Dept Math & Stat, Bundoora, Vic 3086, Australia

关键词: Rate of convergence;    Non-central limit theorems;    Random field;    Long-range dependence;    Rosenblatt distribution;    Generalized Linnik's covariance structure;   

DOI  :  10.1016/j.jmaa.2014.12.016

来源: Elsevier

【 摘 要 】

The main result of the article is the rate of convergence to the Rosenblatt-type distributions in non-central limit theorems. Specifications of the main theorem are discussed for several scenarios. In particular, special attention is paid to the Cauchy, generalized Linnik's, and local global distinguisher random processes and fields. Direct analytical methods are used to investigate the rate of convergence in the uniform metric. Crown Copyright (C) 2014 Published by Elsevier Inc. All rights reserved.

【 授权许可】

Free