Sojourn functionals for spatiotemporal Gaussian random fields with long memory. (March 2023)

• Record Type: Journal Article
• Authors: Leonenko, N. N.; Ruiz-Medina, M. D.
• Is Part Of: Journal of applied probability. Volume 60:Number 1(2023)
• Page Start: 148
• Page End: 165
• Publication Date: 2023-03
• Subjects: Asymptotic normality -- excursion sets -- LRD -- Rosenblatt-type distribution -- spatiotemporal random fields; 60G60 -- 60G15 -- 60F05 -- 60D05; 519.2
• DOI: 10.1017/jpr.2022.30
• Languages: English
• ISSNs: 0021-9002

Abstract

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\geq 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.