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

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