TAIWANESE JOURNAL OF MATHEMATICS
Vol. 4, No. 1, pp. 45-53, March 2000
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SOME FRACTAL PROPERTIES OF BROWNIAN PATHS |
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Narn-Rueih Shieh |
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| Abstract. |
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| In this paper, we survey some recent results concerning the fractal structure of Brownian sample paths. The following aspects are discussed: (1) average densities of Brownian trails and intersections; (2) dimension spectra of Brownian zeros; (3) multifractal properties of Brownian substitutions. |
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Received November 8, 1999.
Communicated by P. Y. Wu.
2000 Mathematics Subject Classification: 60G17.
Key words and phrases:
Brownian motion, self-similarity, Hausdorff dimension, occupation measure, local time measure, intersection measure, average density, dimension spectrum, multifractal.