1 results
Sojourn functionals for spatiotemporal Gaussian random fields with long memory
- Part of
-
- Journal:
- Journal of Applied Probability / Volume 60 / Issue 1 / March 2023
- Published online by Cambridge University Press:
- 09 February 2023, pp. 148-165
- Print publication:
- March 2023
-
- Article
-
- You have access
- HTML
- Export citation
-
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.
