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Prog. Theor. Phys. Vol. 82 No. 3 (1989) pp. 465-470
Letters
Analytical Expression of the Expectation of a Scale Dependent "Length" of a Path of Brownian Motion with Drift
Kazuo Kishimoto
Institute of Socio-Economic Planning, University of Tsukuba, Tukuba 305
(Received February 2, 1989)
Abstract:
The expected path "length" and its associated d.f.d. (differential fractal dimension) are analytically
calculated for the Brownian motion with drift as functions of a scale parameter. These
expressions give precise pictures how the transition of the d.f.d. from 2 to 1 occurs in a fractal
phenomenon.
URL :
http://ptp.ipap.jp/link?PTP/82/465/
DOI : 10.1143/PTP.82.465
References:
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L. S. Cederbaum, E. Haller and P. Pfeifer, Phys. Rev. A31 (1985), 1869[APS].
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M. A. Lopez-Quintela, M. C. Bujan-Nunez and J. C. Perez-Moure, J. Chem. Phys. 88 (1988), 7478, [CrossRef]and references therein.
- B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1982).
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H. Takayasu, J. Phys. Soc. Jpn. 51 (1982), 3057[JPSJ].
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