Evolution of a stochastic system within the framework of Tsallis statistics

The general approach of a nonlinear Fokker-Planck equation is applied to investigate the behavior of main statistical moments of a stochastic system. It was shown that the system described by Tsallis statistics can undergo transitions inherent to multiplicative noise-induced transitions. The scaling laws of motion are defined to identify an anomalous time behavior of the system with multiplicative noise.