Summary
Conditions for the CLT for non-linear functionals of stationary Gaussian sequences are discussed, with special references to the borderline between the CLT and the non-CLT. Examples of the non-CLT for such functionals with the norming factor\(\sqrt N \) are given.
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Giraitis, L., Surgailis, D. CLT and other limit theorems for functionals of Gaussian processes. Z. Wahrscheinlichkeitstheorie verw Gebiete 70, 191–212 (1985). https://doi.org/10.1007/BF02451428
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DOI: https://doi.org/10.1007/BF02451428