La Trobe

Non-central limit theorems and convergence rates

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posted on 2025-04-10, 04:09 authored by Vo Anh, Andriy OlenkoAndriy Olenko, Volodymyr Vaskovych
This paper surveys some recent developments in non-central limit theorems for long-range dependent random processes and fields. We describe an increasing domain framework for asymptotic behavior of functionals of random processes and fields. Recent results on the rate of convergence to the Hermite-type distributions in non-central limit theorems are presented. The use of these results is demonstrated through an application to the case of Rosenblatt-type distributions.

Funding

The first author was supported in part under the Australian Research Council’s Discovery Projects funding scheme (project number DP160101366). The second author was supported in part under the Australian Research Council’s Discovery Projects funding scheme (project number DP160101366) and by the La Trobe University DRP Grant in Mathematical and Computing Sciences.

History

Publication Date

2017-01-01

Journal

Theory of Probability and Mathematical Statistics

Volume

95

Pagination

13p. (p. 3-15)

Publisher

American Mathematical Society

ISSN

0094-9000

Rights Statement

First published in Theor. Probability and Math. Statist. 95 (2017), published by the American Mathematical Society. © 2018 American Mathematical Society. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/

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