A characterization of \(p\)-uniformly smooth Banach spaces and weak laws of large numbers for \(d\)-dimensional adapted arrays

DOI10.1007/s13171-010-0020-7zbMath1213.60086OpenAlexW1995944917MaRDI QIDQ541771

Nguyen Van Huan, Nguyen Van Quang

Publication date: 8 June 2011

Published in: Sankhyā. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13171-010-0020-7

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Probabilistic methods in Banach space theory (46B09) Martingales and classical analysis (60G46) Probability theory on linear topological spaces (60B11)

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Cites Work

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• An extension of the Kolmogorov-Feller weak law of large numbers with an application to the St. Petersburg game
• Stochastic integrals in the plane
• Martingales with values in uniformly convex spaces
• The law of large numbers and the central limit theorem in Banach spaces
• The Hájek-Rényi inequality for Banach space valued martingales and the \(p\) smoothness of Banach spaces
• Uniform convexity in factor and conjugate spaces
• Statistical spatial series modelling II: Some further results on unilateral lattice processes
• An estimate of the convergence rate in the central limit theorem for two-parameter martingale differences
• ON THE WEAK LAW OF LARGE NUMBERS FOR SEQUENCES OF BANACH SPACE VALUED RANDOM ELEMENTS
• WEAK LAW OF LARGE NUMBERS FOR ADAPTED DOUBLE ARRAYS OF RANDOM VARIABLES