Chung's law and the Csáki function
type: Item
instance of: scholarly article
title: Chung's law and the Csáki function
zbMATH Open document ID: 0937.60013
DOI: 10.1023/A:1021678111442
author: Natalia Gorn
author: M. A. Lifshits
published in: Journal of Theoretical Probability
publication date: 2000-01-05T00:00:00Z
review text: The solution to the problem of convergence rate in Chung's functional law of the iterated logarithm is obtained for so-called ``slowest points'' \(h \in C[0,1]\). Namely, the authors find the value \[ {\mathcal L}_h = \liminf_{T \to \infty} (\log\log T)^{2/3} \Biggl\|\frac{W(T\cdot)}{(2T\log\log T)^{1/2}} - h\Biggr\| \] where \(W\) is a standard Wiener process, \(||\cdot||\) is the sup-norm in the space \(C[0,1]\). This is a generalization of results of \textit{E. Csáki} [Z. Wahrscheinlichkeitstheorie Verw. Geb. 54, 287-301 (1980; Zbl 0441.60027) and in: Limit theorems in probability and statistics. Colloq. Math. Soc. J. Bolyai 57, 83-93 (1990; Zbl 0719.60033)] proved both for piecewise-linear function \(h\) and quadratic function \(h\). The problem of finding \({\mathcal L}_h\) is related to the study of some functional of Wiener process in a strip.
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 1309014
zbMATH Keywords: Wiener process
zbMATH Keywords: large deviation
reviewed by: Alexander V. Bulinski
MaRDI profile type: Publication
full work available at URL: a:1021678111442
OpenAlex ID: W8957533
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description: scientific article; zbMATH DE number 1309014