A mixture-type limit theorem for nonlinear functions of Gaussian sequences

DOI10.1007/BF01258745zbMath0728.60040OpenAlexW1983674565MaRDI QIDQ805059

Tze-Chien Sun, Hwai-Chung Ho

Publication date: 1991

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01258745

zbMATH Keywords

correlation functionGaussian stationary processmultiple Wiener-Itô integralmixture-type limit theorem

Mathematics Subject Classification ID

Gaussian processes (60G15) Stationary stochastic processes (60G10)

Cites Work

• Unnamed Item
• Limiting distributions of nonlinear vector functions of stationary Gaussian processes
• Central limit theorems for non-linear functionals of Gaussian fields
• Remarks on limit theorems for nonlinear functionals of Gaussian sequences
• A central limit theorem for non-instantaneous filters of a stationary Gaussian process
• Multiple Wiener-Ito integrals. With applications to limit theorems
• Necessary conditions for nonlinear functionals of Gaussian processes to satisfy central limit theorems
• Convergence of integrated processes of arbitrary Hermite rank
• Non-central limit theorems for non-linear functional of Gaussian fields