The empirical process of a short-range dependent stationary sequence under Gaussian subordination

DOI10.1007/BF01303800zbMath0838.60030OpenAlexW2074242499MaRDI QIDQ1908536

Jan Mielniczuk, Sándor Csörgö

Publication date: 27 May 1996

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01303800

zbMATH Keywords

Gaussian processempirical distribution functionstationary Gaussian sequencecontinuous marginal distribution

Mathematics Subject Classification ID

Order statistics; empirical distribution functions (62G30) Functional limit theorems; invariance principles (60F17)

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Cites Work

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• The empirical process of some long-range dependent sequences with an application to U-statistics
• Central limit theorems for non-linear functionals of Gaussian fields
• Positively correlated normal variables are associated
• The asymptotic distribution theory of the empiric cdf for mixing stochastic processes
• A Glivenko-Cantelli lemma and weak convergence for empirical processes of associated sequences
• A note on empirical processes of strong-mixing sequences
• CLT and other limit theorems for functionals of Gaussian processes
• 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
• A Note on Weak Convergence of Empirical Processes for Sequences of $\phi$- Mixing Random Variables

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