Central limit theorems for non-linear functionals of Gaussian fields |
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Authors: | Péter Breuer Péter Major |
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Institution: | Institute for Psychology of the Hungarian Academy of Sciences, Budapest, Hungary;Mathematical Institute of the Hungarian Academy of Sciences, Budapest, Hungary |
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Abstract: | In the present paper it is shown that the central limit theorem holds for some non-linear functionals of stationary Gaussian fields if the correlation function of the underlying field tends fast enough to zero. The results are formulated in terms of the Hermite rank of the functional and of the rate of the correlation function. Then we show an example when the limit field is self-similar and Gaussian but not necessarily consisting of independent elements. |
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Keywords: | 60F 60G Self-similar Gaussian fields diagram formula Hermite rank |
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