A weak law for normed weighted sums of random elements in Rademacher type \(p\) Banach spaces

DOI10.1016/0047-259X(91)90083-EzbMath0735.60004MaRDI QIDQ1176230

Andrew Rosalsky, André Adler, Robert Lee Taylor

Publication date: 25 June 1992

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

weak law of large numbersBanach space valued random variables

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Probability theory on linear topological spaces (60B11) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (6)

Characterization of typep Banach spaces by the weak law of large numbers ⋮ Some Strong Laws of Large Numbers for Banach Space Valued Summands Irrespective of Their Joint Distributions ⋮ Almost sure convergence of the general Jamison weighted sum of \({\mathcal B}\)-valued random variables ⋮ Some Strong and Weak Limit Theorems for Weighted Sums of i.i.d. Banach Space Valued Random Elements with Slowly Varying Weights ⋮ One-sided limit theorems for sums of multidimensional indexed random variables ⋮ On the limiting behavior of randomly weighted partial sums

Cites Work

• Generalized one-sided laws of the iterated logarithm for random variables barely with or without finite mean
• Some applications of isoperimetric methods to strong limit theorems for sums of independent random variables
• On the weak law of large numbers for normed weighted sums of i.i.d. random variables
• Strong laws of large numbers for fields of Banach space valued random variables
• Stabilité de sommes pondérées de variables aléatoires vectorielles. (Stability of weighted sums of vector random variables)
• Stochastic convergence of weighted sums of random elements in linear spaces
• Inequalities for B-valued random vectors with applications to the strong law of large numbers
• Iterated logarithm laws for asymmetric random variables barely with or without finite mean
• Some stability results for vector valued random variables
• Strong laws of large numbers for weighted sums of random elements in normed linear spaces
• On Almost Sure Behavior of Sums of Independent B<scp>anach</scp> Space Valued Random Variables
• Some general strong laws for weighted sums of stochastically dominated random variables
• A Limit Theoerm for Random Variables with Infinite Moments
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