Level sets of multiparameter Brownian motions

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Title:	Level sets of multiparameter Brownian motions
Author:	Nualart, Eulàlia; Mountford, Thomas S.
Abstract:	We use Girsanov's theorem to establish a conjecture of Khoshnevisan, Xiao and Zhong that ϕ(r)=rN−d/2(loglog(1r))d/2 is the exact Hausdorff measure function for the zero level set of an N-parameter d-dimensional additive Brownian motion. We extend this result to a natural multiparameter version of Taylor and Wendel's theorem on the relationship between Brownian local time and the Hausdorff ϕ-measure of the zero set.
Abstract:	The research of Mountford TS is partially supported by the NSF Grant DMS. The research of Nualart E is supported by the Fonds National Suisse.
Subject(s):	-Local times -Hausdorff measure -Level sets -Additive Brownian motion
Rights:	This article is published with a Creative Commons Attribution Licence (CC BY 2.5) http://creativecommons.org/licenses/by/2.5/legalcode
Document type:	Article Article - Published version
Published by:	Institute of Mathematical Statistics (IMS)
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