Asymptotic behavior of functionals of cyclic long-range dependent random fields |
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Authors: | Boris Klykavka Andriy Olenko Matthew Vicendese |
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Institution: | 1. Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine ??KPI,?? 37, Peremohy Ave., Kyiv, 03056, Ukraine 2. Department of Mathematics and Statistics, La Trobe University, Victoria, 3086, Australia
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Abstract: | Long-range dependent random fields with spectral densities, which are unbounded at some frequencies, are investigated. We demonstrate new examples of covariance functions, which do not exhibit a regular varying asymptotic behavior at infinity. However, the variances of averaged functionals of these fields are regularly varying. The limit theorems for weighted functionals of cyclic long-range dependent fields are obtained. The order of normalizing constants and relations between the weight functions and singularities in non-degenerative asymptotics are discussed. |
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