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arXiv · hep-ph/0405202

Power-law tails from multiplicative noise

Tamas S. Biro·Antal Jakovac
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Abstract

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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Tamas S. Biro, Antal Jakovac. 2004-05-21. Power-law tails from multiplicative noise. https://doi.org/10.1103/physrevlett.94.132302

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