Invariance principles for partial sum processes and empirical processes indexed by sets

DOI10.1007/BF01845991zbMath0591.60009OpenAlexW2075573456MaRDI QIDQ1074942

Walter Philipp, Gregory J. Morrow

Publication date: 1986

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01845991

zbMATH Keywords

almost sure approximationapproximation of empirical processesGaussian partial sum processes indexed by sets

Mathematics Subject Classification ID

Functional limit theorems; invariance principles (60F17) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items

Laws of the iterated logarithm for partial sum processes indexed by functions ⋮ Parallel and bootstrapped stochastic approximation

Cites Work

• Some limit theorems for empirical processes (with discussion)
• Functional law of the iterated logarithm and uniform central limit theorem for partial-sum processes indexed by sets
• Weak and \(L^p\)-invariance principles for sums of \(B\)-valued random variables
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• Approximation theorems for independent and weakly dependent random vectors
• Sample functions of the Gaussian process
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• Approximation of rectangular sums of B-valued random variables
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• Invariance principles for sums of Banach space valued random elements and empirical processes
• [https://portal.mardi4nfdi.de/wiki/Publication:4084475 Convergence en loi et lois du logarithme it�r� pour les vecteurs gaussiens]
• An almost sure invariance principle for the empirical distribution function of mixing random variables
• The Law of the Iterated Logarithm for Brownian Motion in a Banach Space
• The Existence of Probability Measures with Given Marginals
• Inequalities with Applications to the Weak Convergence of Random Processes with Multi-Dimensional Time Parameters
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