Some mean convergence theorems for the maximum of normed double sums of Banach space valued random elements

DOI10.1007/s10114-024-2669-1zbMATH Open1546.60066MaRDI QIDQ6596312

Le Van Thanh, Andrew Rosalsky, Nguyen Thi Thuy

Publication date: 2 September 2024

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

zbMATH Keywords

double summean convergenceRademacher type \(p\) Banach spaceBanach space valued random element\(M\)-dependent random elements

Mathematics Subject Classification ID

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

Cites Work

• \(L^r\) convergence for \(B\)-valued random elements
• On the laws of large numbers for double arrays of independent random elements in Banach spaces
• On Marcinkiewicz SLLN in Banach spaces
• Convergence in the \(p\)th-mean and some weak laws of large numbers for weighted sums of random elements in separable normed linear spaces
• The law of large numbers and the central limit theorem in Banach spaces
• A note on the stochastic domination condition and uniform integrability with applications to the strong law of large numbers
• A new type of compact uniform integrability with application to degenerate mean convergence of weighted sums of Banach space valued random elements
• 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
• Strong and Weak Laws of Large Numbers for Double Sums of Independent Random Elements in Rademacher TypepBanach Spaces
• The Kronecker lemmas for multiple series and some applications
• Some degenerate mean convergence theorems for Banach space valued random elements
• Convergence of randomly weighted sums of Banach space valued random elements and uniform integrability concerning the random weights

Related Items (1)

Maximal inequalities for normed double sums of random elements in martingale type \(p\) Banach spaces with applications to degenerate mean convergence of the maximum of normed sums

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