Limit theorems for additive functionals of stationary fields, under integrability assumptions on the higher order spectral densities

We obtain central limit theorems for additive functionals of stationary fields under integrability conditions on the higher-order spectral densities. The proofs are based on the Hölder–Young–Brascamp–Lieb inequality.

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Bibliographic Details
Published in:Stochastic processes and their applications 2015-04, Vol.125 (4), p.1629-1652
Main Authors: Avram, Florin, Leonenko, Nikolai, Sakhno, Ludmila
Format: Article
Language:English
Subjects:
Asymptotic normality
Higher-order spectral densities
Hölder–Young–Brascamp–Lieb inequality
Integral of random fields
Mathematics
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Description
Summary:We obtain central limit theorems for additive functionals of stationary fields under integrability conditions on the higher-order spectral densities. The proofs are based on the Hölder–Young–Brascamp–Lieb inequality.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2014.11.010