A functional central limit theorem for strongly mixing sequences of random variables

DOI10.1007/BF00532665zbMath0558.60032MaRDI QIDQ3223621

Norbert Herrndorf

Publication date: 1985

Published in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete (Search for Journal in Brave)

zbMATH Keywords

functional central limit theoremstrongly mixing sequences of random variables

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Functional limit theorems; invariance principles (60F17)

Related Items (17)

The functional central limit theorem under the strong mixing condition ⋮ Quantifying the data-dredging bias in structural break tests ⋮ The asymptotic distribution of CUSUM estimator based on α-mixing sequences ⋮ Central limit theorems and uniform laws of large numbers for arrays of random fields ⋮ Modeling long term return distribution and nonparametric market risk estimation ⋮ Convergence of \(U\)-processes in Hölder spaces with application to robust detection of a changed segment ⋮ On a theorem of gordin ⋮ TESTING STRUCTURAL CHANGE IN PARTIALLY LINEAR MODELS ⋮ Estimation of the variance for strongly mixing sequences ⋮ Estimation of the limit variance for sums under a new weak dependence condition ⋮ Testing for a unit root under errors with just barely infinite variance ⋮ The central limit theorem for Tukey's 3R smoother ⋮ Asymptotics for weakly dependent errors-in-variables ⋮ A functional limit theorem for dependent sequences with infinite variance stable limits ⋮ Complete convergence for \(\alpha{}\)-mixing sequences ⋮ Mixing Conditions, Central Limit Theorems, and Invariance Principles: A Survey of the Literature with Some New Results on Heteroscedastic Sequences ⋮ Random Walks with Drift – A Sequential Approach

Cites Work

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• Corrigendum to central limit theorems for dependent variables. I
• Central Limit Theorems for dependent variables. I
• The invariance principle for ϕ-mixing sequences
• Invariance principles for dependent variables
• Convergence of Distributions Generated by Stationary Stochastic Processes
• Functional central limit theorems for strictly stationary processes satisfying the strong mixing condition
• Some Limit Theorems for Stationary Processes

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