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.
@article{bwmeta1.element.bwnjournal-article-fmv147i2p157bwm,
author = {Dmitry Dolgopyat and Vadim Sidorov},
title = {Multifractal properties of the sets of zeroes of Brownian paths},
journal = {Fundamenta Mathematicae},
volume = {146},
year = {1995},
pages = {157-171},
zbl = {0837.60077},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv147i2p157bwm}
}
Dolgopyat, Dmitry; Sidorov, Vadim. Multifractal properties of the sets of zeroes of Brownian paths. Fundamenta Mathematicae, Tome 146 (1995) pp. 157-171. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv147i2p157bwm/
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