On rate of convergence in non-central limit theorems
Probability
2017-03-20 v1
Abstract
The main result of this paper is the rate of convergence to Hermite-type distributions in non-central limit theorems. To the best of our knowledge, this is the first result in the literature on rates of convergence of functionals of random fields to Hermite-type distributions with ranks greater than 2. The results were obtained under rather general assumptions on the spectral densities of random fields. These assumptions are even weaker than in the known convergence results for the case of Rosenblatt distributions. Additionally, L\'{e}vy concentration functions for Hermite-type distributions were investigated.
Keywords
Cite
@article{arxiv.1703.05900,
title = {On rate of convergence in non-central limit theorems},
author = {Vo Anh and Nikolai Leonenko and Andriy Olenko and Volodymyr Vaskovych},
journal= {arXiv preprint arXiv:1703.05900},
year = {2017}
}
Comments
28 pages. arXiv admin note: text overlap with arXiv:1412.6860