Theory of Probability and Mathematical Statistics
Non-central limit theorems and convergence rates
Vo Anh, Andriy Olenko, V. Vaskovych
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Abstract: This paper surveys some recent developments in non-central limit theorems for long-range dependent random processes and fields. We describe an increasing domain framework for asymptotic behavior of functionals of random processes and fields. Recent results on the rate of convergence to the Hermite-type distributions in non-central limit theorems are presented. The use of these results is demonstrated through an application to the case of Rosenblatt-type distributions.
Keywords: Non-central limit theorems, Rate of convergence, Random field, Long-range dependence, Rosenblatt-type distributions.
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