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MiS Preprint

Brownian motion of fractal particles: Lévy flights from white noise

Kiran M. Kolwankar


We generalise the Langevin equation with Gaussian white noise by replacing the velocity term by a local fractional derivative. The solution of this equation is a Lévy process. We further consider the Brownian motion of a fractal particle, for example, a colloidal aggregate or a biological molecule and argue that it leads to a Lévy flight. This effect can also be described using the local fractional Langevin equation. The implications of this development to other complex data series are discussed.

Nov 14, 2005
Nov 14, 2005
05.40.-a, 05.10.Gg, 05.45.Df, 87.10.+e
brownian motion, fractal, fractional calculus, levy process

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2005 Repository Open Access
Kiran Murlidhar Kolwankar

Brownian motion of fractal particles : Lévy flights from white noise