Distributional limit theorems over a stationary Gaussian sequence of random vectors.

DOI10.1016/S0304-4149(99)00122-2zbMath1045.60019WikidataQ127937944 ScholiaQ127937944MaRDI QIDQ1877507

Miguel A. Arcones

Publication date: 7 September 2004

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

Hermite polynomialslong-range dependencestationary Gaussian sequence

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10)

Related Items (7)

Parametric estimation of long memory multivariate Gaussian random fields ⋮ Limiting spectral distribution of sample autocovariance matrices ⋮ Sojourn measures of Student and Fisher-Snedecor random fields ⋮ Asymptotic behavior of weakly dependent aggregated processes ⋮ On a localization property of wavelet coefficients for processes with stationary increments, and applications. I. Localization with respect to shift ⋮ Limit Theorems for Aggregated Linear Processes ⋮ Estimation of harmonic component in regression with cyclically dependent errors

Uses Software

• longmemo

Cites Work

• Central limit theorems for non-linear functionals of Gaussian fields
• Multiple Wiener-Ito integrals. With applications to limit theorems
• Limit theorems for nonlinear functionals of a stationary Gaussian sequence of vectors
• Weak convergence to fractional brownian motion and to the rosenblatt process
• Law of the iterated logarithm for sums of non-linear functions of Gaussian variables that exhibit a long range dependence
• Convergence of integrated processes of arbitrary Hermite rank
• Non-central limit theorems for non-linear functional of Gaussian fields
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