Tsallis statistics and Langevin equation with multiplicative noise in different orders of prescription

Kwok Sau Fa

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arXiv · 1207.5172

Tsallis statistics and Langevin equation with multiplicative noise in different orders of prescription

Kwok Sau Fa

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Abstract

Usually discussions on the question of interpretation in the Langevin equation with multiplicative white noise are limited to the Ito and Stratonovich prescriptions. In this work, a Langevin equation with multiplicative white noise and its Fokker-Planck equation are considered. From this Fokker-Planck equation a connection between the stationary solution and the Tsallis distribution is obtained for different orders of prescription in discretization rule for the stochastic integrals; the Tsallis index $q$ and the prescription parameter (\lambda) are determined with the drift and diffusion coefficients. The result is quite general. For application, one shows that the Tsallis distribution can be described by a class of population growth models subject to the linear multiplicative white noise.

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Kwok Sau Fa. 2012-07-21. Tsallis statistics and Langevin equation with multiplicative noise in different orders of prescription. https://arxiv.org/abs/1207.5172

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