Summary
We prove limit theorems for sums of non-linear functionals of Gaussian sequences. In certain cases we obtain a non-Gaussian limit with a norming factor n α, 0<α<1/2. The class of functionals we are investigating is a natural enlargement of the class investigated by M. Rosenblatt in [7]. We prove our results by refining the method of the paper [3].
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This research was done during the author's visit to Göttingen University. It was supported by the Deutsche Forschungsgemeinschaft
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Major, P. Limit theorems for non-linear functionals of Gaussian sequences. Z. Wahrscheinlichkeitstheorie verw Gebiete 57, 129–158 (1981). https://doi.org/10.1007/BF00533717
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DOI: https://doi.org/10.1007/BF00533717