Asymptotic expansions for central limit theorems for general linear stochastic processes. I: General theorems on rates of convergence

DOI10.1002/mma.1670010208zbMath0419.60016OpenAlexW2088102856MaRDI QIDQ3852864

Paul L. Butzer, Ursula Gather

Publication date: 1979

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.1670010208

zbMATH Keywords

asymptotic expansionscentral limit theoremorder of convergencegeneral stochastic processLindeberg-type condition

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Estimation and detection in stochastic control theory (93E10) Signal detection and filtering (aspects of stochastic processes) (60G35) Generalized stochastic processes (60G20)

Related Items (3)

A retrospective on research visits of Paul Butzer's Aachen research group to Eastern Europe and Tenerife ⋮ Asymptotic expansions for central limit theorems for general linear stochastic processes. II: Models of the general random noise and pulse train processes ⋮ Convergence rates in multivariate robust outlier identification

Cites Work

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• On a class of stochastic processes which are closed under linear transformations
• On the Independence of Linear Functionals of Linear Processes
• Convergence Properties of the Sample Mean and Sample Correlation for a Class of Pulse Trains
• Moments of a Stopping Rule Related to the Central Limit Theorem
• Central Limit Theorems for Conditionally Linear Random Processes
• Asymptotic Expansions for a Class of Distribution Functions
• The Lipschitz condition of a function and Fejer means of Fourier series

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