On Gaussian approximation of Hilbert space valued discrete time martingales

DOI10.1007/BF00995990zbMath0877.60007MaRDI QIDQ1897889

Alfredas Račkauskas

Publication date: 18 September 1995

Published in: Lithuanian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

seminorm\(H\)-valued random elementsconditional covariance operatorHilbert space martingale central limit theorem

Mathematics Subject Classification ID

Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Cites Work

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• Uniform convexity and the distribution of the norm for a Gaussian measure
• Uniform bound in the central limit theorem for Banach space valued dependent random variables
• On the rate of convergence in the central limit theorem for martingales with discrete and continuous time
• Exact convergence rates in some martingale central limit theorems
• Nonuniform estimates in the central limit theorem in Banach spaces
• Summation of Laplace series in the class of distributions
• Distribution function inequalities for martingales

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