Open Access
November 2019 On rate of convergence in non-central limit theorems
Vo Anh, Nikolai Leonenko, Andriy Olenko, Volodymyr Vaskovych
Bernoulli 25(4A): 2920-2948 (November 2019). DOI: 10.3150/18-BEJ1075


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, Lévy concentration functions for Hermite-type distributions were investigated.


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Vo Anh. Nikolai Leonenko. Andriy Olenko. Volodymyr Vaskovych. "On rate of convergence in non-central limit theorems." Bernoulli 25 (4A) 2920 - 2948, November 2019.


Received: 1 March 2018; Revised: 1 September 2018; Published: November 2019
First available in Project Euclid: 13 September 2019

zbMATH: 07110116
MathSciNet: MR4003569
Digital Object Identifier: 10.3150/18-BEJ1075

Keywords: Hermite-type distribution , long-range dependence , Non-central limit theorems , Random field , rate of convergence

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

Vol.25 • No. 4A • November 2019
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