Singular properties of high-order spectral densities of supOU processes

Kovtun, Anastasiia, Leonenko, Mykola ORCID: https://orcid.org/0000-0003-1932-4091 and Pepelyshev, Andrey ORCID: https://orcid.org/0000-0001-5634-5559 2025. Singular properties of high-order spectral densities of supOU processes. Communications in Nonlinear Science and Numerical Simulation 10.1016/j.cnsns.2025.109459

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Abstract

This paper investigates the properties of high-order spectral densities and high-order cumulants of superpositions of Ornstein-Uhlenbeck (supOU) processes. As is well known, the long-range dependence of a stochastic process is typically characterized by the second-order spectral density or correlation function. We introduce the property of high-order long-range dependence using high-order spectral densities and cumulants. Sufficient conditions are derived for the supOU process to exhibit high-order long-range dependence. A numerical study of supOU processes with Dickman and gamma marginals is presented to illustrate the theoretical findings.

Item Type:	Article
Date Type:	Published Online
Status:	In Press
Schools:	Schools > Mathematics
Publisher:	Elsevier
ISSN:	1007-5704
Date of First Compliant Deposit:	28 October 2025
Date of Acceptance:	27 October 2025
Last Modified:	13 Nov 2025 10:33
URI:	https://orca.cardiff.ac.uk/id/eprint/181935

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