Bernoulli

  • Bernoulli
  • Volume 25, Number 4A (2019), 2920-2948.

On rate of convergence in non-central limit theorems

Vo Anh, Nikolai Leonenko, Andriy Olenko, and Volodymyr Vaskovych

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

Article information

Source
Bernoulli, Volume 25, Number 4A (2019), 2920-2948.

Dates
Received: March 2018
Revised: September 2018
First available in Project Euclid: 13 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.bj/1568362047

Digital Object Identifier
doi:10.3150/18-BEJ1075

Keywords
Hermite-type distribution long-range dependence non-central limit theorems random field rate of convergence

Citation

Anh, Vo; Leonenko, Nikolai; Olenko, Andriy; Vaskovych, Volodymyr. On rate of convergence in non-central limit theorems. Bernoulli 25 (2019), no. 4A, 2920--2948. doi:10.3150/18-BEJ1075. https://projecteuclid.org/euclid.bj/1568362047


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