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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.

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