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: | 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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