On the strong law of large numbers and \(\mathcal L_p\)-convergence for double arrays of random elements in \(p\)-uniformly smooth Banach spaces

DOI10.1016/j.spl.2009.05.014zbMath1173.60314OpenAlexW2084918689MaRDI QIDQ842951

Nguyen Van Quang, Nguyen Van Huan

Publication date: 28 September 2009

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

Full work available at URL: https://doi.org/10.1016/j.spl.2009.05.014

zbMATH Keywords

double arrays of random elements\(\mathcal L_p\)-convergencesome strong 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) (L^p)-limit theorems (60F25)

Related Items (9)

Unnamed Item ⋮ Inequalities for sums of adapted random fields in Banach spaces and their application to strong law of large numbers ⋮ A new family of convex weakly compact valued random variables in Banach space and applications to laws of large numbers ⋮ Strong laws of large numbers for adapted arrays of set-valued and fuzzy-valued random variables in Banach space ⋮ Strong laws for blockwise martingale difference arrays in Banach spaces ⋮ A Hájek-Rényi-type maximal inequality and strong laws of large numbers for multidimensional arrays ⋮ Rate of complete convergence for maximums of moving average sums of martingale difference fields in Banach spaces ⋮ Unnamed Item ⋮ Some strong laws of large number for double array of random upper semicontinuous functions in convex combination spaces

Cites Work

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• A mean convergence theorem and weak law for arrays of random elements in martingale type \(p\) Banach spaces
• Mean convergence theorems and weak laws of large numbers for weighted sums of random variables under a condition of weighted integrability
• Strong laws of large numbers for \(r\)-dimensional arrays of random variables
• Abstract martingale convergence theorems
• Strong and Weak Laws of Large Numbers for Double Sums of Independent Random Elements in Rademacher TypepBanach Spaces

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