On the tail behaviour of the distribution function of multiple stochastic integrals
type: Item
instance of: scholarly article
title: On the tail behaviour of the distribution function of multiple stochastic integrals
zbMATH Open document ID: 0628.60065
DOI: 10.1007/BF00334204
publication date: 1988-01-01T00:00:00Z
review text: Let \(F_ n(u)\) denote the empirical distribution function of a sample of i.i.d. random variables with uniform distribution on [0,1]. Define ū\({}^ *_ n(u)=\sqrt{n}| F_ n(u)-u|\), and consider the integrals \[ I(t)=\int ^{t}_{0}\int ^{1}_{0}...\int ^{1}_{0}f(u_ 1,...,u_ s){\bar \mu}^ *_ n(du_ 1)...\mu ^ *_ n(du_ s), \] where f is a bounded measurable function. We give a good upper bound on the probability P(\(\underline{\sup}_{0\leq t\leq 1}| I(t)| \geq x)\). An analogous estimate is given for multiple integrals with respect to a Poisson process.
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60G55
zbMATH DE Number: 4022295
zbMATH Keywords: empirical distribution
zbMATH Keywords: multiple integrals with respect to a Poisson process
author: P. Major
MaRDI profile type: Publication
cites work: Strong embedding of the estimator of the distribution function under random censorship
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
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description: scientific article; zbMATH DE number 4022295