Rate of complete convergence for maximums of moving average sums of martingale difference fields in Banach spaces

DOI10.1016/j.spl.2012.06.014zbMath1264.60009OpenAlexW1983732686MaRDI QIDQ712532

Ta Cong Son, Le Van Dung, Dang Hung Thang

Publication date: 17 October 2012

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spl.2012.06.014

zbMATH Keywords

complete convergence\(p\)-uniformly smooth Banach spacesMarcinkiewicz-Zygmund strong laws of larger numbersMartingale difference fields

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 (2)

On convergence of moving average series of martingale differences fields taking values in Banach spaces ⋮ The Brunk-Prokhorov strong law of large numbers for fields of martingale differences taking values in a Banach space

Cites Work

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• On the strong law of large numbers and \(\mathcal L_p\)-convergence for double arrays of random elements in \(p\)-uniformly smooth Banach spaces
• A note on the rate of complete convergence for maximums of partial sums for moving average processes in Rademacher type Banach spaces
• Strong laws of large numbers for random fields in martingale type \(p\) Banach spaces
• An asymmetric Marcinkiewicz-Zygmund LLN for random fields
• Complete convergence of moving average processes
• The law of large numbers and the central limit theorem in Banach spaces
• Almost sure convergence of the general Jamison weighted sum of \({\mathcal B}\)-valued random variables
• Abstract martingale convergence theorems
• Complete Convergence and the Law of Large Numbers

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