Some strong laws of large numbers for blockwise martingale difference sequences in martingale type \(p\) Banach spaces

DOI10.1007/s10114-012-0378-7zbMath1271.60012OpenAlexW2076077859MaRDI QIDQ1757963

Le Van Thanh, Andrew Rosalsky

Publication date: 7 November 2012

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-012-0378-7

zbMATH Keywords

strong law of large numbersalmost sure convergenceblockwise martingale difference sequencemartingale type \(p\) Banach spacesequence of Banach space valued random elements

Mathematics Subject Classification ID

Strong limit theorems (60F15) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Cites Work

• On the strong limit theorems for double arrays of blockwise \(M\)-dependent random variables
• Strong laws for blockwise \(\mathcal M\)-dependent random fields
• Stochastic convergence of weighted sums of random elements in linear spaces
• Martingales with values in uniformly convex spaces
• The law of large numbers and the central limit theorem in Banach spaces
• Convergence of weighted sums of tight random elements
• Strong laws of large numbers for arrays of orthogonal random elements in Banach spaces
• Strong laws of large numbers for weighted sums of random elements in normed linear spaces
• A weak law with random indices for randomly weighted sums of random elements in martingale type \(p\) Banach spaces.
• On the strong law of large numbers for \(d\)-dimensional arrays of random variables
• Abstract martingale convergence theorems
• Geometry and probability in Banach spaces
• Strong Limit Theorems for Blockwise m-Dependent and Blockwise Quasiorthogonal Sequences of Random Variables
• Some general strong laws for weighted sums of stochastically dominated random variables
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