Marcinkiewicz-Zygmund type law of large numbers for double arrays of random elements in Banach spaces

DOI10.1134/S1995080209040118zbMath1227.60008MaRDI QIDQ639455

Nguyen Duy Tien, Le Van Dung, Thuntida Ngamkham, Andrei I. Volodin

Publication date: 21 September 2011

Published in: Lobachevskii Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Marcinkiewicz-Zygmund inequalitydouble arrays of random elementsmartingale type \(p\) Banach spacesRademacher type \(p\) Banach spacesstrong and \(L_p\) laws of large numbers

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Strong limit theorems (60F15) Probability theory on linear topological spaces (60B11) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items

Complete convergence in mean for double arrays of random variables with values in Banach spaces., A Hájek-Rényi-type maximal inequality and strong laws of large numbers for multidimensional arrays, Strong laws of large numbers for random fields in martingale type \(p\) Banach spaces

Cites Work

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• The law of large numbers and the central limit theorem in Banach spaces
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• Precise asymptotics in some strong limit theorems for multidimensionally indexed random variables
• Abstract martingale convergence theorems
• Strong and Weak Laws of Large Numbers for Double Sums of Independent Random Elements in Rademacher TypepBanach Spaces
• An elementary proof of the strong law of large numbers
• MARCINKIEWICZ-ZYGMUND LAW OF LARGE NUMBERS FOR BLOCKWISE ADAPTED SEQUENCES
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