The \(p\)-variation of partial sum processes and the empirical process

DOI10.1214/aop/1022855756zbMath0927.62049OpenAlexW2025584671MaRDI QIDQ1307491

Jinghua Qian

Publication date: 14 December 1999

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1022855756

zbMATH Keywords

empirical processpartial sum processes\(p\)-variation norm

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Order statistics; empirical distribution functions (62G30) Sums of independent random variables; random walks (60G50) Monotonic functions, generalizations (26A48) Functions of bounded variation, generalizations (26A45)

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Cites Work

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• The strong p-variation of martingales and orthogonal series
• Fréchet differentiability, \(p\)-variation and uniform Donsker classes
• Kolmogorov's law of the iterated logarithm for Banach space valued random variables
• The \(p\)-variation of partial sum processes and the empirical process
• The order of the remainder in derivatives of composition and inverse operators for \(p\)-variation norms
• Exact asymptotic estimates of Brownian path variation
• An inequality of the Hölder type, connected with Stieltjes integration
• Invariance principles for sums of Banach space valued random elements and empirical processes
• La variation d'ordre p des semi-martingales
• An Estimate Concerning the Kolmogroff Limit Distribution

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