Strong and Weak Laws of Large Numbers for Double Sums of Independent Random Elements in Rademacher TypepBanach Spaces

DOI10.1080/07362990600958770zbMath1112.60002OpenAlexW2061861696MaRDI QIDQ3423708

Andrew Rosalsky, Le Van Thanh

Publication date: 15 February 2007

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

Full work available at URL: https://doi.org/10.1080/07362990600958770

zbMATH Keywords

Banach spacealmost sure convergenceconvergence in probabilitydouble array of independent random elementsdouble sumsrandom indicesreal separable Rademacher typestrong and weak laws of large numbers

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Strong limit theorems (60F15) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (19)

On the strong law of large numbers and \(\mathcal L_p\)-convergence for double arrays of random elements in \(p\)-uniformly smooth Banach spaces ⋮ Strong laws of large numbers for WAPND Banach-valued random elements ⋮ Unnamed Item ⋮ A strong limit theorem for double arrays of dependent random variables ⋮ Unnamed Item ⋮ Weak laws of large numbers of double sums of independent random elements in Rademacher type \(p\) and stable type \(p\) Banach spaces ⋮ Marcinkiewicz-Zygmund type law of large numbers for double arrays of random elements in Banach spaces ⋮ Mean convergence and weak laws of large numbers for multidimensional arrays of random elements ⋮ A new family of convex weakly compact valued random variables in Banach space and applications to laws of large numbers ⋮ On the weak laws of large numbers for weighted sums of dependent identically distributed random vectors in Hilbert spaces ⋮ Strong laws of large numbers for adapted arrays of set-valued and fuzzy-valued random variables in Banach space ⋮ On Almost Sure and Mean Convergence of Normed Double Sums of Banach Space Valued 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 ⋮ Strong laws of large numbers for double sums of Banach space valued random elements ⋮ On the weak law of large numbers for double adapted arrays of random elements in \(p\)-uniformly smooth Banach space ⋮ Almost sure convergence for double arrays of block-wiseM-dependent random elements in Banach spaces ⋮ Strong laws of large numbers for \(\mathbb B\)-valued random fields

Cites Work

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• Stochastic convergence of weighted sums of random elements in linear spaces
• Convergence of reversed martingales with multidimensional indices
• The law of large numbers and the central limit theorem in Banach spaces
• Convergence of weighted sums of tight random elements
• Weak laws with random indices for arrays of random elements in Rademacher type \(p\) Banach spaces
• Strong laws of large numbers for \(r\)-dimensional arrays of random variables
• The ergodic theorem
• Absence of a wetting transition for a pinned harmonic crystal in dimensions three and larger
• Maximal inequalities for partial sums of independent random vectors with multi dimensional time parameters
• An elementary proof of the strong law of large numbers
• Proof of the Ergodic Theorem
• REPRESENTATIONS OF WEAK AND STRONG INTEGRALS IN BANACH SPACES
• The Homogeneous Chaos

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