Limit theorems for the nonlinear functional of stationary Gaussian processes

DOI10.1006/jmva.2001.1986zbMath1016.60021OpenAlexW2042076461MaRDI QIDQ1599236

Samir Ben Hariz

Publication date: 27 July 2003

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmva.2001.1986

zbMATH Keywords

Gaussian processesempirical processesfunctional central limit theoremsweakly dependent processesRosenthal type inequalities

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Functional limit theorems; invariance principles (60F17)

Related Items (12)

Functional limit theorems for Volterra processes and applications to homogenization* ⋮ Continuous Breuer-Major theorem: tightness and nonstationarity ⋮ Sojourn measures of Student and Fisher-Snedecor random fields ⋮ Asymptotic covariances for functionals of weakly stationary random fields ⋮ Reduction principle for functionals of vector random fields ⋮ Continuous Breuer-Major theorem for vector valued fields ⋮ Variations and estimators for self-similarity parameters via Malliavin calculus ⋮ Reduction principle for functionals of strong-weak dependent vector random fields ⋮ The functional Breuer-Major theorem ⋮ Integrated functionals of normal and fractional processes ⋮ Generating diffusions with fractional Brownian motion ⋮ Functional limit theorems for the fractional Ornstein-Uhlenbeck process

Cites Work

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• Weak convergence for weighted empirical processes of dependent sequences
• Central limit theorems for non-linear functionals of Gaussian fields
• Invariance principles for absolutely regular empirical processes
• Limit theorems for nonlinear functionals of a stationary Gaussian sequence of vectors
• The empirical process of a short-range dependent stationary sequence under Gaussian subordination
• 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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