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A central limit theorem for non-linear functionals of stationary Gaussian vector processes

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  • Sánchez de Naranjo, M. V.

Abstract

Let Xn = (Xn1, ..., Xnd) be a stationary Gaussian vector process, such that the correlation matrix tends fast to 0. Suppose H is a d-dimensional function and define . It is shown that ZN(H) has a Gaussian limiting distribution.

Suggested Citation

  • Sánchez de Naranjo, M. V., 1995. "A central limit theorem for non-linear functionals of stationary Gaussian vector processes," Statistics & Probability Letters, Elsevier, vol. 22(3), pages 223-230, February.
    • Handle: RePEc:eee:stapro:v:22:y:1995:i:3:p:223-230
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    References listed on IDEAS

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    1. Ho, Hwai-Chung & Sun, Tze-Chien, 1987. "A central limit theorem for non-instantaneous filters of a stationary Gaussian process," Journal of Multivariate Analysis, Elsevier, vol. 22(1), pages 144-155, June.
    2. Denaranjo, M. V. S., 1993. "Non-central Limit Theorems for Non-linear Functionals of k Gaussian Fields," Journal of Multivariate Analysis, Elsevier, vol. 44(2), pages 227-255, February.
    3. Breuer, Péter & Major, Péter, 1983. "Central limit theorems for non-linear functionals of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 425-441, September.
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    Cited by:

    1. Andriy Olenko & Dareen Omari, 2020. "Reduction Principle for Functionals of Vector Random Fields," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 573-598, June.
    2. Zhao, Zhibiao & Wu, Wei Biao, 2007. "Asymptotic theory for curve-crossing analysis," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 862-877, July.

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