General theorems on Little-\(\mathcal O\) rates of closeness of two weighted sums of independent Hilbert space valued random variables with applications

DOI10.1016/0047-259X(79)90054-XzbMath0428.60028MaRDI QIDQ1137303

L. Hahn, M. Th. Roeckerath, Paul L. Butzer

Publication date: 1979

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

zbMATH Keywords

central limit theoremweak law of large numbersstable limit theoremHilbert space valued random variablesrates of weak convergence

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Rate of convergence, degree of approximation (41A25) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (2)

o-rates of closeness of two weighted random sums of dependent Banach- valued random variables ⋮ Central limit theorem and weak law of large numbers with rates for martingales in Banach spaces

Cites Work

• Some results of probability measures on linear topological vector spaces with an application to Strassen's log log law
• On the rate of approximation in the central limit theorem
• Berry-Esseen estimates in Hilbert space and an application to the law of the iterated logarithm
• Stochastic convergence of weighted sums in normed linear spaces
• General theorems on rates of convergence in distribution of random variables II. Applications to the stable limit laws and weak law of large numbers
• Domains of attraction of stable measures on a Hilbert space
• On stable distributions in Hilbert space
• Some Structure Theorems for the Symmetric Stable Laws
• Stable probability measures on Banach spaces
• On the Closeness of the Distributions of Two Sums of Independent Random Variables
• A representation theorem for symmetric stable processes and stable measures on H
• Harmonic analysis on Hilbert space
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