Level sets of multiparameter Brownian motions

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dc.contributor.author	Nualart, Eulàlia
dc.contributor.author	Mountford, Thomas S.
dc.date	2004
dc.identifier.citation	Mountford TS, Nualart E. Level sets of multiparameter Brownian motions. Electron J Probab. 2004;9(20): 594-614. DOI: 10.1214/EJP.v9-169
dc.identifier.citation	1083-6489
dc.identifier.citation	http://dx.doi.org/10.1214/EJP.v9-169
dc.identifier.uri	http://hdl.handle.net/10230/34388
dc.format	application/pdf
dc.language.iso	eng
dc.publisher	Institute of Mathematical Statistics (IMS)
dc.relation	Electronic Journal of Probability. 2004;9(20): 594-614.
dc.rights	This article is published with a Creative Commons Attribution Licence (CC BY 2.5)
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by/2.5/legalcode
dc.subject	Local times
dc.subject	Hausdorff measure
dc.subject	Level sets
dc.subject	Additive Brownian motion
dc.title	Level sets of multiparameter Brownian motions
dc.type	info:eu-repo/semantics/article
dc.type	info:eu-repo/semantics/publishedVersion
dc.description.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.
dc.description.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.

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