Level Sets of Multiparameter Brownian Motions

Eulalia Nualart (Université de Paris 6)
Thomas S. Mountford (Ecole Polytechnique Fédérale de Lausanne)


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.

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Pages: 594-614

Publication Date: September 13, 2004

DOI: 10.1214/EJP.v9-169


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