On the central limit theorem and law of the iterated logarithm for stationary processes with applications to linear processes

DOI10.1016/0304-4149(95)00038-9zbMath0834.60026OpenAlexW1969550941MaRDI QIDQ1904552

Ryozo Yokoyama

Publication date: 1 February 1996

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

Full work available at URL: https://doi.org/10.1016/0304-4149(95)00038-9

zbMATH Keywords

law of the iterated logarithmcentral limit theoremmartingale difference sequencesstationary linear processesstrictly stationary processes

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10) Measure-preserving transformations (28D05) Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17)

Related Items

Random central limit theorems for linear processes with weakly dependent innovations ⋮ Strong invariance principles for dependent random variables ⋮ The limit law of the iterated logarithm for linear processes ⋮ Law of the iterated logarithm for stationary processes ⋮ On linear processes with dependent innovations ⋮ Asymptotics for moving average processes with dependent innovations

Cites Work

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• Approximating martingales and the central limit theorem for strictly stationary processes
• Invariance principles for the law of the iterated logarithm for martingales and processes with stationary increments
• Regularly varying functions in the theory of simple branching processes
• On the central limit theorem and iterated logarithm law for stationary processes
• The Lindeberg-Levy Theorem for Martingales
• The Hartman-Wintner Law of the Iterated Logarithm for Martingales
• A Central Limit Theorem for a Class of Dependent Random Variables
• Limit theorems for sums of dependent random variables

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