On stationarity properties of generalized Hermite-type processes

Donhauzer, Illia; Olenko, Andriy

doi:10.1080/17442508.2020.1844709

On stationarity properties of generalized Hermite-type processes

journal contribution

posted on 2025-03-05, 03:50 authored by Illia DonhauzerIllia Donhauzer, Andriy OlenkoAndriy Olenko

The paper investigates properties of generalized Hermite-type processes that arise in non-central limit theorems for integral functionals of long-range dependent random fields. The case of increasing multidimensional domain asymptotics is studied. Three approaches to investigate the properties of these processes are discussed. Contrary to the classical one-dimensional case, it is shown that for any choice of a multidimensional observation window the generalized Hermite-type process has non-stationary increments.

Funding

A. Olenko was partially supported under the Australian Research Council Discovery Projects funding scheme [project number DP160101366].

History

Publication Date

2021-11-01

Journal

Stochastics

Volume

93

Issue

7

Pagination

15p. (p. 1107-1121)

Publisher

Taylor & Francis

ISSN

1744-2508

Rights Statement

© 2020 Informa UK Limited, trading as Taylor & Francis Group This is an Accepted Manuscript version of the following article, accepted for publication in Stochastics. Donhauzer, I., & Olenko, A. (2020). On stationarity properties of generalized Hermite-type processes. Stochastics, 93(7), 1107–1121. https://doi.org/10.1080/17442508.2020.1844709. It is deposited under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way.