Central limit theorem and weak law of large numbers with rates for martingales in Banach spaces

DOI10.1016/0047-259X(83)90027-1zbMath0515.60014MaRDI QIDQ1051974

L. Hahn, M. Th. Roeckerath, Paul L. Butzer

Publication date: 1983

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

zbMATH Keywords

rates of convergencecentral limit theoremweak law of large numbersdecomposability of random variablesmartingale difference sequences in Banach spaces

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Central limit and other weak theorems (60F05) Convergence of probability measures (60B10) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (9)

\(U\)-statistics in Banach spaces ⋮ The rate of convergence in the central limit theorem for non-stationary dependent random vectors ⋮ o-rates of closeness of two weighted random sums of dependent Banach- valued random variables ⋮ Rate of convergence in the martingale central limit theorem in the space C(S) ⋮ The generalized Trotter operator and weak convergence of dependent random variables in different probability metrics ⋮ A retrospective on research visits of Paul Butzer's Aachen research group to Eastern Europe and Tenerife ⋮ On the convergence rate in martingale CLT in Hilbert spaces ⋮ Uniform bounds in the central limit theorem for \(C(S)\) valued martingales ⋮ Weax convergence of probability reasures in C_b(C[0,1) equipped with rates]

Cites Work

• General theorems on Little-\(\mathcal O\) rates of closeness of two weighted sums of independent Hilbert space valued random variables with applications
• On the rate of approximation in the central limit theorem for dependent random variables and random vectors
• Berry-Esseen estimates in Hilbert space and an application to the law of the iterated logarithm
• Convergence of some functionals of sums of independent random variables in a Banach space
• The law of large numbers and the central limit theorem in Banach spaces
• General theorems on rates of convergence in distribution of random variables I. General limit theorems
• Dependent central limit theorems and invariance principles
• Abstract martingale convergence theorems
• The central limit theorem for dependent random variables
• Les fonctions aléatoires comme éléments aléatoires dans les espace de Banach
• Explicit bounds for the departure from normality of sums of dependent random variables
• On the rate of convergence to normality for sums of dependent random variables
• On central limit theorems for martingale triangular arrays
• Approximation of Distributions of Sums of Independent Random Variables with Values in Infinite-Dimensional Spaces
• On the Rate of Convergence in the Central Limit Theorem in Certain Banach Spaces
• The Lindeberg-Levy Theorem for Martingales
• On the Departure from Normality of a Certain Class of Martingales
• Central limit theorems for martingales and for processes with stationary increments using a Skorokhod representation approach
• A Central Limit Theorem for a Class of Dependent Random Variables
• Convergence de la répartition empirique vers la répartition théorique
• An elementary proof of the central limit theorem
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