Approximation of rectangular sums of B-valued random variables

DOI10.1007/BF00535494zbMath0477.60005MaRDI QIDQ3935197

Gregory J. Morrow

Publication date: 1981

Published in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete (Search for Journal in Brave)

zbMATH Keywords

Brownian sheetfunctional law of the iterated logarithmWiener measure on a separable Banach space

Mathematics Subject Classification ID

Gaussian processes (60G15) Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (5)

A remark on the multiparameter law of the iterated logarithm ⋮ Parallel and bootstrapped stochastic approximation ⋮ Approximation of sums of random variables with multiindexes ⋮ Invariance principles for partial sum processes and empirical processes indexed by sets ⋮ Central limit theorem for linearly dependent fields of continuous elements

Cites Work

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• Almost sure invariance principles for partial sums of mixing B-valued random variables
• Kolmogorov's law of the iterated logarithm for Banach space valued random variables
• Approximation theorems for independent and weakly dependent random vectors
• Sample functions of the \(N\)-parameter Wiener process
• Some Strassen-type laws of the iterated logarithm for multiparameter stochastic processes with independent increments
• Lectures in modern analysis and applications. II
• Approximation of partial sums of i.i.d.r.v.s when the summands have only two moments
• A Smoothing Inequality for Estimates of the Lévy–Prokhorov Distance
• The Law of the Iterated Logarithm for Brownian Motion in a Banach Space
• An invariance principle for the law of the iterated logarithm

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