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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
100/2005

Brownian motion of fractal particles: Lévy flights from white noise

Kiran M. Kolwankar

Abstract

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.

Received:
14.11.05
Published:
14.11.05
PACS:
05.40.-a, 05.10.Gg, 05.45.Df, 87.10.+e
Keywords:
brownian motion, fractal, fractional calculus, levy process

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Preprint
2005 Repository Open Access
Kiran Murlidhar Kolwankar

Brownian motion of fractal particles : Lévy flights from white noise