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Level Sets of Multiparameter Brownian Motions


 
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1. Title Title of document Level Sets of Multiparameter Brownian Motions
 
2. Creator Author's name, affiliation, country Eulalia Nualart; Université de Paris 6
 
2. Creator Author's name, affiliation, country Thomas S. Mountford; Ecole Polytechnique Fédérale de Lausanne
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Local times; Hausdorff measure; level sets; additive Brownian motion
 
3. Subject Subject classification 60G60; 60G15; 60G17
 
4. Description Abstract We use Girsanov's theorem to establish a conjecture of Khoshnevisan, Xiao and Zhong that $\phi(r) = r^{N-d/2} (\log \log (\frac{1}{r}))^{d/2}$ 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 $\phi$-measure of the zero set.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSF Grant DMS; Fonds National Suisse
 
7. Date (YYYY-MM-DD) 2004-09-13
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/169
 
10. Identifier Digital Object Identifier 10.1214/EJP.v9-169
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 9
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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