Hausdorff and packing measures of the level sets of iterated Brownian motion
type: Item
instance of: scholarly article
title: Hausdorff and packing measures of the level sets of iterated Brownian motion
zbMATH Open document ID: 0935.60066
DOI: 10.1023/A:1021669809625
published in: Journal of Theoretical Probability
publication date: 2000-04-25T00:00:00Z
review text: Iterated Brownian motion is defined as \(Z(t)=X(Y(t))\) where \(X\) and \(Y\) are independent (two-sided) Brownian motions. The exact Hausdorff dimension gauge of the level sets of iterated Bronwian motion is determined to be \(\varphi(x)=x^{3/4}[\log\log(1/x)]^{3/4}\). This result generalizes earlier work of \textit{K. Burdzy} and \textit{D. Khoshnevisan} [in: Séminaire de probabilités XXIX. Lect. Notes Math. 1613, 231-236 (1995; Zbl 0853.60061)]. The paper also contains a slightly less precise result about the packing gauge of the level sets. The proofs rely on an accurate analysis of the local times.
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 28A78
Mathematics Subject Classification ID: 60J55
zbMATH DE Number: 1309010
zbMATH Keywords: Hausdorff measure
zbMATH Keywords: packing measure
zbMATH Keywords: exact Hausdorff dimension
zbMATH Keywords: exact packing dimension
zbMATH Keywords: gauge function
zbMATH Keywords: iterated Brownian motion
zbMATH Keywords: local time
author: Yueyun Hu
MaRDI profile type: Publication
full work available at URL: a:1021669809625
OpenAlex ID: W155763475
description: scientific article; zbMATH DE number 1309010