Geodesic
Multifractal properties of the sets of zeroes of Brownian paths
Fundamenta Mathematicae, Tome 147 (1995) no. 2, pp. 157-171.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We study Brownian zeroes in the neighborhood of which one can observe a non-typical growth rate of Brownian excursions. We interpret the multifractal curve for the Brownian zeroes calculated in [6] as the Hausdorff dimension of certain sets. This provides an example of the multifractal analysis of a statistically self-similar random fractal when both the spacing and the size of the corresponding nested sets are random.
DOI : 10.4064/fm_1995_147_2_1_157_171
Keywords: independent random variables, Brownian motion, local time, Hausdorff dimension, self-similarity

Dmitry Dolgopyat 1 ; Vadim Sidorov 1

1 
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Dmitry Dolgopyat; Vadim Sidorov. Multifractal properties of the sets of zeroes of Brownian paths. Fundamenta Mathematicae, Tome 147 (1995) no. 2, pp. 157-171. doi : 10.4064/fm_1995_147_2_1_157_171. http://geodesic.mathdoc.fr/articles/10.4064/fm_1995_147_2_1_157_171/

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