Power-law tails from multiplicative noise

Details Power-law tails from multiplicative noise Power-law tails from multiplicative noise

2004-05-21

arxiv.org/abs/hep-ph/0405202v1

Phys.Rev.Lett. 94 (2005) 132302

Physics

High Energy Physics

High Energy Physics - Phenomenology

4 pages, LaTeX, revtex4 style, 2 figures

Scientific paper

10.1103/PhysRevLett.94.132302

We show that the well-known Langevin equation, modeling the Brownian motion and leading to a Gaussian stationary distribution of the corresponding Fokker-Planck equation, is changed by the smallest multiplicative noise. This leads to a power-law tail of the distribution at large enough momenta. At finite ratio of the correlation strength for the multiplicative and additive noise the stationary energy distribution becomes exactly the Tsallis distribution.

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