Sojourn functionals for spatiotemporal Gaussian random fields with long memory

Leonenko, N. N. ORCID: https://orcid.org/0000-0003-1932-4091 and Ruiz-Medina, M. D. 2023. Sojourn functionals for spatiotemporal Gaussian random fields with long memory. Journal of Applied Probability 60 (1) , pp. 148-165. 10.1017/jpr.2022.30

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Abstract

This paper addresses the asymptotic analysis of sojourn functionals of spatiotemporal Gaussian random fields with long-range dependence (LRD) in time, also known as long memory. Specifically, reduction theorems are derived for local functionals of nonlinear transformation of such fields, with Hermite rank m≥1, under general covariance structures. These results are proven to hold, in particular, for a family of nonseparable covariance structures belonging to the Gneiting class. For m=2, under separability of the spatiotemporal covariance function in space and time, the properly normalized Minkowski functional, involving the modulus of a Gaussian random field, converges in distribution to the Rosenblatt-type limiting distribution for a suitable range of values of the long-memory parameter.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Applied Probability Trust
ISSN:	0021-9002
Date of First Compliant Deposit:	24 February 2022
Date of Acceptance:	22 February 2022
Last Modified:	16 Nov 2024 17:30
URI:	https://orca.cardiff.ac.uk/id/eprint/147805

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