TAIWANESE JOURNAL OF MATHEMATICS

Vol. 4, No. 1, pp. 45-53,  March 2000

 

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    SOME FRACTAL PROPERTIES OF BROWNIAN PATHS

 

Narn-Rueih Shieh

 

Abstract.

              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.