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Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)



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

T. Alodat, A. Olenko

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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 same distributions under certain assumptions. The result is applied to integrals over a multidimensional rectangle with a constant weight function.

Keywords: Random fields, Hermite-type distributions, non-central limit theorems, longrange dependence, weighted nonlinear functionals.

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