High-level moving excursions for spatiotemporal Gaussian random fields with long range dependence

Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091 and Ruiz-Medina, M. Dolorez 2025. High-level moving excursions for spatiotemporal Gaussian random fields with long range dependence. Journal of Statistical Physics 192 , 19. 10.1007/s10955-025-03396-y

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Abstract

The asymptotic behavior of an extended family of integral geometric random functionals, including spatiotemporal Minkowski functionals under moving levels, is analyzed in this paper. Specifically, sojourn measures of spatiotemporal long-range dependence (LRD) Gaussian random fields are considered in this analysis. The limit results derived provide general reduction principles under increasing domain asymptotics in space and time. The case of time-varying thresholds is also studied. Thus, the family of morphological measures considered allows the statistical and geometrical analysis of random physical systems displaying structural changes over time. Motivated by cosmological applications, the derived results are applied to the context of sojourn measures of spatiotemporal spherical Gaussian random fields. The results are illustrated for some families of spatiotemporal Gaussian random fields displaying complex spatiotemporal dependence structures.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Mathematics
Publisher:	Springer
ISSN:	0022-4715
Date of First Compliant Deposit:	22 January 2025
Date of Acceptance:	5 January 2025
Last Modified:	05 Feb 2025 15:15
URI:	https://orca.cardiff.ac.uk/id/eprint/175061

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