Uniform bound in the central limit theorem for Banach space valued dependent random variables

DOI10.1016/0047-259X(86)90085-0zbMath0606.60010MaRDI QIDQ1084741

WanSoo T. Rhee, Michel Talagrand

Publication date: 1986

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

rate of convergencemartingale differencesconditional covariance structureTrotter's method

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (11)

\(U\)-statistics in Banach spaces ⋮ On the rate of convergence in the martingale CLT ⋮ On Gaussian approximation of Hilbert space valued discrete time martingales ⋮ The rate of convergence in the central limit theorem for non-stationary dependent random vectors ⋮ On the conditional covariance condition in the martingale CLT ⋮ On distribution of the norm for normal random elements in the space of continuous functions ⋮ On a multidimensional martingale with given conditional covariance structure ⋮ Extremes of weighted Brownian bridges in increasing dimension ⋮ On the convergence rate in martingale CLT in Hilbert spaces ⋮ Uniform bounds in the central limit theorem for \(C(S)\) valued martingales ⋮ Uniform convexity and the distribution of the norm for a Gaussian measure

Cites Work

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• Convex measures on locally convex spaces
• Berry-Esseen estimates in Hilbert space and an application to the law of the iterated logarithm
• The law of large numbers and the central limit theorem in Banach spaces
• Les fonctions aléatoires comme éléments aléatoires dans les espace de Banach
• On Berry-Esseen type bounds for m-dependent random variables valued in certain banach spaces
• On the rate of convergence to normality for sums of dependent random variables
• On the Rate of Convergence in the Central Limit Theorem in Certain Banach Spaces
• On the Berry-Esseen theorem

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