Multifractal properties of the sets of zeroes of Brownian paths
Dmitry Dolgopyat; Vadim Sidorov
Fundamenta Mathematicae (1995)
- Volume: 147, Issue: 2, page 157-171
- ISSN: 0016-2736
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topDolgopyat, Dmitry, and Sidorov, Vadim. "Multifractal properties of the sets of zeroes of Brownian paths." Fundamenta Mathematicae 147.2 (1995): 157-171. <http://eudml.org/doc/212080>.
@article{Dolgopyat1995,
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.},
author = {Dolgopyat, Dmitry, Sidorov, Vadim},
journal = {Fundamenta Mathematicae},
keywords = {independent random variables; Brownian motion; local time; Hausdorff dimension; self-similarity},
language = {eng},
number = {2},
pages = {157-171},
title = {Multifractal properties of the sets of zeroes of Brownian paths},
url = {http://eudml.org/doc/212080},
volume = {147},
year = {1995},
}
TY - JOUR
AU - Dolgopyat, Dmitry
AU - Sidorov, Vadim
TI - Multifractal properties of the sets of zeroes of Brownian paths
JO - Fundamenta Mathematicae
PY - 1995
VL - 147
IS - 2
SP - 157
EP - 171
AB - 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.
LA - eng
KW - independent random variables; Brownian motion; local time; Hausdorff dimension; self-similarity
UR - http://eudml.org/doc/212080
ER -
References
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- [5] K. Ito and H. McKean, Diffusion Processes and their Sample Paths, Springer, Berlin, 1965. Zbl0127.09503
- [6] G. M. Molchan, Multi-mono-fractal properties of Brownian zeroes, Proc. Russian Acad. Sci. 335 (1994), 424-427.
- [7] S. J. Taylor, The α-dimensional measure on the graph and set of zeroes of a Brownian path, Proc. Cambridge Philos. Soc. 51 (1953), 31-39.
- [8] S. J. Taylor, The measure theory of random fractals, Math. Proc. Cambridge Philos. Soc. 100 (1986), 383-406. Zbl0622.60021
- [9] S. J. Taylor and J. G. Wendel, The exact Hausdorff measure of the zero set of a stable process, Z. Wahrsch. Verw. Gebiete 6 (1966), 170-180. Zbl0178.52702
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