Chung's law of the iterated logarithm for iterated Brownian motion
type: Item
instance of: scholarly article
title: Chung's law of the iterated logarithm for iterated Brownian motion
zbMATH Open document ID: 0859.60025
author: D. Khoshnevisan
author: Thomas M. Lewis
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1996-07-08T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77538
review text: Let \(X\) and \(Y\) be independent, standard Brownian motions. It is shown that the iterated Brownian motion \(\{Z(t), t\geq 0\}\), where \(Z(t)=X(|Y(t)|)\), obeys \[ \liminf_{t\to\infty} {(\log\log t)^{3/4}\over t^{1/4}}\sup_{0\leq s\leq t}|Z(s)|={\pi^{3/2}e^{3/4}\over 2^{11/4}} \] almost surely. This result is reminiscent of \textit{K. L. Chung's} law of the iterated logarithm [Trans. Am. Math. Soc. 64, 205-233 (1948; Zbl 0032.17102)].
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 60G18
zbMATH DE Number: 898065
zbMATH Keywords: iterated Brownian motion
zbMATH Keywords: law of the iterated logarithm
reviewed by: R. James Tomkins
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 898065