Mean Convergence Theorems with or without Random Indices for Randomly Weighted Sums of Random Elements in Rademacher TypepBanach Spaces

DOI10.1081/SAP-120024708zbMath1038.60025MaRDI QIDQ4421486

Andrei I. Volodin, Andrew Rosalsky, Sreehari Maddipatla

Publication date: 27 August 2003

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

zbMATH Keywords

weak law of large numbersweighted sumsrandom indicesRademacher type \(p\) Banach space

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)

Related Items

\(L^r\) convergence for \(B\)-valued random elements, Some mean convergence theorems for weighted sums of Banach space valued random elements, Mean convergence theorem for multidimensional arrays of random elements in Banach spaces, Complete convergence theorems for weighted row sums from arrays of random elements in Rademacher type p and martingale type p Banach spaces

Cites Work

• On the almost sure convergence of randomly weighted sums of random elements
• Limit theorems for randomly weighted sums of random elements in normed linear spaces
• The law of large numbers and the central limit theorem in Banach spaces
• Convergence of weighted sums of tight random elements
• On the weak law of large numbers for arrays
• A mean convergence theorem and weak law for arrays of random elements in martingale type \(p\) Banach spaces
• Weak laws with random indices for arrays of random elements in Rademacher type \(p\) Banach spaces
• On convergence in r-mean of some first passage times and randomly indexed partial sums
• A weak law with random indices for randomly weighted sums of random elements in martingale type \(p\) Banach spaces.
• On the weak law for randomly indexed partial sums for arrays of random elements in martingale type \(p\) Banach spaces
• Stochastic convergence of randomly weighted sums of random elements
• On weak and Moments Convergence of Randomly Indexed Sums
• Convergence of randomly weighted sums of Banach space valued random elements and uniform integrability concerning the random weights