| Issue |
ESAIM: PS
Volume 24, 2020
|
|
|---|---|---|
| Page(s) | 315 - 340 | |
| DOI | https://doi.org/10.1051/ps/2020006 | |
| Published online | 27 July 2020 | |
Non-central limit theorems for functionals of random fields on hypersurfaces
Department of Mathematics and Statistics, La Trobe University Melbourne,
Melbourne
3086, Australia.
* Corresponding author: a.olenko@latrobe.edu.au
Received:
26
March
2019
Accepted:
20
January
2020
This paper derives non-central asymptotic results for non-linear integral functionals of homogeneous isotropic Gaussian random fields defined on hypersurfaces in ℝd. We obtain the rate of convergence for these functionals. The results extend recent findings for solid figures. We apply the obtained results to the case of sojourn measures and demonstrate different limit situations.
Mathematics Subject Classification: 60G60 / 60F05 / 60G12
Key words: Non-central limit theorems / random field / long-range dependence / hermite-type distribution / sojourn measures
© EDP Sciences, SMAI 2020
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