This paper derives non-central asymptotic results for non-linear integral functionals of homogeneous isotropic Gaussian random fields defined on hypersurfaces in d. 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.
Publication Date
2020-07-27Journal
ESAIM: Probability and StatisticsVolume
24Pagination
26p. (p. 315-340)Publisher
EDP SciencesISSN
1292-8100Rights Statement
© EDP Sciences, SMAI 2020
This document is the Accepted Manuscript version of a Published Work that appeared in final form as: Non-central limit theorems for functionals of random fields on hypersurfaces - ESAIM: PS - Volume 24, 2020 - https://doi.org/10.1051/ps/2020006 - Andriy Olenko* and Volodymyr Vaskovych.
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Distribution Rights: This permission is granted for the purpose of reuse in “Non-central limit theorems for functionals of random fields on hypersurfaces” and does not extend to any other forms of distribution or reproduction beyond what is customary for the journal's dissemination practices.
