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Limit Theorems for the Non-linear Functional of Stationary Gaussian Processes

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  • Hariz, Samir Ben

Abstract

In this paper we consider two functional limit theorems for the non-linear functional of the stationary Gaussian process satisfying short range dependence conditions: the functional CLT for partial sum processes and the uniform CLT for a special class of functions. To carry out the proofs, we develop Rosenthal type inequalities for the functional of Gaussian processes.

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  • Hariz, Samir Ben, 2002. "Limit Theorems for the Non-linear Functional of Stationary Gaussian Processes," Journal of Multivariate Analysis, Elsevier, vol. 80(2), pages 191-216, February.
    • Handle: RePEc:eee:jmvana:v:80:y:2002:i:2:p:191-216
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    References listed on IDEAS

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    1. 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. Johann Gehringer & Xue-Mei Li, 2022. "Functional Limit Theorems for the Fractional Ornstein–Uhlenbeck Process," Journal of Theoretical Probability, Springer, vol. 35(1), pages 426-456, March.

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