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Level Sets of Multiparameter Brownian Motions
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Eulalia Nualart, Université de Paris 6
Thomas S. Mountford, Ecole Polytechnique Fédérale de Lausanne
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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.
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Full text: PDF
Pages: 594-614
Published on: September 13, 2004
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Electronic Journal of Probability. ISSN: 1083-6489 |
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