Weak convergence of weighted additive functionals of long-range dependent fields

Alodat, T.; Olenko, A.

doi:10.1090/tpms/1044

Weak convergence of weighted additive functionals of long-range dependent fields

Authors: T. Alodat and A. Olenko
Translated by: The authors
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 97 (2017).
Journal: Theor. Probability and Math. Statist. 97 (2018), 1-16
MSC (2010): Primary 60G60; Secondary 60G12, 60F05
DOI: https://doi.org/10.1090/tpms/1044
Published electronically: February 21, 2019
MathSciNet review: 3745995
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Abstract | References | Similar Articles | Additional Information

Abstract: We provide asymptotic results for the distribution of weighted nonlinear functionals of Gaussian field with long-range dependence. We also show that integral functionals and the corresponding additive functionals have the same distributions under certain assumptions. The result is applied to integrals over a multidimensional rectangle with a constant weight function.

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