On Almost Sure and Mean Convergence of Normed Double Sums of Banach Space Valued Random Elements

DOI10.1080/07362990701420142zbMath1124.60007OpenAlexW2011430259MaRDI QIDQ3592752

Le Van Thanh, Andrew Rosalsky

Publication date: 21 September 2007

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07362990701420142

zbMATH Keywords

almost sure convergenceRademacher type \(p\)real separable Banach space\(p\)-orthogonaldouble arrayindependent random elementsnormed double sumsconvergence in mean of order \(p\)

Mathematics Subject Classification ID

Strong limit theorems (60F15) Probability theory on linear topological spaces (60B11) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12) (L^p)-limit theorems (60F25)

Related Items (12)

On the strong laws of large numbers for sequences of blockwise pairwise and coordinatewise negatively dependent random vectors in Hilbert spaces ⋮ On the strong limit theorems for double arrays of blockwise \(M\)-dependent random variables ⋮ On almost certain convergence of double series of random elements and the rate of convergence of tail series ⋮ On the weak laws of large numbers for sums of negatively associated random vectors in Hilbert spaces ⋮ On the \(L^1\)-convergence for double arrays of blockwise \(M\)-pairwise negatively dependent random variables ⋮ Mean convergence and weak laws of large numbers for multidimensional arrays of random elements ⋮ On complete convergence in mean for double sums of independent random elements in Banach spaces ⋮ On complete convergence in mean for double sums of independent random elements in Banach spaces ⋮ On the laws of large numbers for double arrays of independent random elements in Banach spaces ⋮ Unnamed Item ⋮ Strong laws of large numbers for double sums of Banach space valued random elements ⋮ Almost sure convergence for double arrays of block-wiseM-dependent random elements in Banach spaces

Cites Work

• Stochastic convergence of weighted sums of random elements in linear spaces
• The law of large numbers and the central limit theorem in Banach spaces
• Convergence of weighted sums of tight random elements
• Marcinkiewicz laws and convergence rates in the law of large numbers for random variables with multidimensional indices
• Strong laws of large numbers for arrays of orthogonal random elements in Banach spaces
• Strong and Weak Laws of Large Numbers for Double Sums of Independent Random Elements in Rademacher TypepBanach Spaces
• Inequalities with Applications to the Weak Convergence of Random Processes with Multi-Dimensional Time Parameters

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