La Trobe

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

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posted on 2025-04-10, 05:42 authored by Tareq AlodatTareq Alodat, Andriy OlenkoAndriy Olenko
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.

Funding

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.

History

Publication Date

2018-01-01

Journal

Theory of Probability and Mathematical Statistics

Volume

97

Pagination

1-16

Publisher

American Mathematical Society

ISSN

0094-9000

Rights Statement

First published in Theor. Probability and Math. Statist. 97 (2018), published by the American Mathematical Society. © 2019 American Mathematical Society. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/

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