Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
157-171
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-11-05
Twórcy
autor
- Mathematics Department, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08540, U.S.A.
autor
- Chair of Probability Theory, Moscow State University, Department of Mathematics and Mechanics, 119 899 Moscow, Russia
Bibliografia
- [1] K. Evertz, Laplacian fractals, Ph.D. thesis, Yale University, 1989.
- [2] K. J. Falconer, The Geometry of Fractal Sets, Cambridge University Press, 1985.
- [3] W. Feller, An Introduction to Probability Theory and its Applications, Vol. 2, Wiley, 1970.
- [4] I. A. Ibragimov and Yu. V. Linnik, Independent and Stationary Sequences of Random Variables, Wolters-Noordhoff, Groningen, 1971.
- [5] K. Ito and H. McKean, Diffusion Processes and their Sample Paths, Springer, Berlin, 1965.
- [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.
- [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.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
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