Multifractal properties of the sets of zeroes of Brownian paths

Volume 147 / 1995

Dmitry Dolgopyat, Vadim Sidorov Fundamenta Mathematicae 147 (1995), 157-171 DOI: 10.4064/fm_1995_147_2_1_157_171

Abstract

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.

Authors

  • Dmitry Dolgopyat
  • Vadim Sidorov

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