 Inner rates of coverage of Strassen type sets by increments of the uniform empirical and quantile processesPhilippe Berthet Stochastic Processes and their Applications, 2005, vol. 115, issue 3, 493-537 Abstract: We establish Chung-Mogulskii type functional laws of the iterated logarithm for medium and large increments of the uniform empirical and quantile processes. This gives the ultimate sup-norm distance between various sets of properly normalized empirical increment processes and a fixed function of the relevant cluster sets. Interestingly, we obtain the exact rates and constants even for most functions of the critical border of Strassen type balls and further introduce minimal entropy conditions on the locations of the increments under which the fastest rates are achieved with probability one. Similar results are derived for the Brownian motion and other related processes. Keywords: Empirical; processes; Clustering; rates; Chung-Mogulskii; functional; laws; Strassen's; law; of; the; iterated; logarithm; Wiener; process (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:115:y:2005:i:3:p:493-537 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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