Non-central limit theorems for functionals of random fields on hypersurfaces

Olenko, Andriy; Vaskovych, Volodymyr

doi:10.1051/ps/2020006

Olenko, Andriy ; Vaskovych, Volodymyr

ESAIM: Probability and Statistics, Tome 24 (2020), pp. 315-340.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

Résumé

This paper derives non-central asymptotic results for non-linear integral functionals of homogeneous isotropic Gaussian random fields defined on hypersurfaces in $ℝ^{d}$ . 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.

MR Zbl

DOI : 10.1051/ps/2020006

Classification : 60G60, 60F05, 60G12
Mots-clés : Non-central limit theorems, random field, long-range dependence, hermite-type distribution, sojourn measures

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     author = {Olenko, Andriy and Vaskovych, Volodymyr},
     title = {Non-central limit theorems for functionals of random fields on hypersurfaces},
     journal = {ESAIM: Probability and Statistics},
     pages = {315--340},
     publisher = {EDP-Sciences},
     volume = {24},
     year = {2020},
     doi = {10.1051/ps/2020006},
     mrnumber = {4126979},
     zbl = {1461.60036},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ps/2020006/}
}

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Olenko, Andriy; Vaskovych, Volodymyr. Non-central limit theorems for functionals of random fields on hypersurfaces. ESAIM: Probability and Statistics, Tome 24 (2020), pp. 315-340. doi : 10.1051/ps/2020006. https://www.numdam.org/articles/10.1051/ps/2020006/

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