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Theory of Probability and Mathematical Statistics

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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: 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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Additional Information

T. Alodat
Affiliation: Department of Mathematics and Statistics, La Trobe University, Melbourne, Victoria, 3086, Australia
Email: Alodat.t@students.latrobe.edu.au

A. Olenko
Affiliation: Department of Mathematics and Statistics, La Trobe University, Melbourne, Victoria, 3086, Australia
Email: a.olenko@latrobe.edu.au

DOI: https://doi.org/10.1090/tpms/1044
Keywords: Random fields, Hermite-type distributions, noncentral limit theorems, long-range dependence, weighted nonlinear functionals
Received by editor(s): September 19, 2017
Published electronically: February 21, 2019
Additional Notes: Supported in part under the Australian Research Council’s Discovery Project funding scheme (project number DP160101366) and in part by the La Trobe University DRP Grant in Mathematical and Computing Sciences.
Dedicated: This paper is dedicated to the 85th anniversary of Professor M. Yadrenko’s birth
Article copyright: © Copyright 2019 American Mathematical Society