1207.5172 (Kwok Sau Fa)

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

Kwok Sau Fa

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.

View original: http://arxiv.org/abs/1207.5172