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Limit theorems for filtered long-range dependent random fields

Alodat, Tareq, Leonenko, Nikolai ORCID: and Olenko, Andriy 2020. Limit theorems for filtered long-range dependent random fields. Stochastics: An International Journal of Probability and Stochastic Processes 92 (8) , pp. 1175-1196. 10.1080/17442508.2019.1691211

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This article investigates general scaling settings and limit distributions of functionals of filtered random fields. The filters are defined by the convolution of non-random kernels with functions of Gaussian random fields. The case of long-range dependent fields and increasing observation windows is studied. The obtained limit random processes are non-Gaussian. Most known results on this topic give asymptotic processes that always exhibit non-negative auto-correlation structures and have the self-similar parameter H∈(12,1). In this work we also obtain convergence for the case H∈(0,12) and show how the Hurst parameter H can depend on the shape of the observation windows. Various examples are presented.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: Taylor & Francis
ISSN: 1744-2508
Date of First Compliant Deposit: 8 November 2019
Date of Acceptance: 7 November 2019
Last Modified: 07 Nov 2023 01:02

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