Time evolution of averages in dynamical systems driven by noise

Abstract

This paper presents a description of the time evolution of the averages of the Markov process in a wide range of noise intensity. The exact expression of the time scale of the evolution of an average has been obtained. It has been demonstrated numerically that for purely noise-induced transitions (transitions over potential barriers) the time evolution of the mean coordinate is a simple exponent with a good precision, even for the case where the potential barrier height is comparable or smaller than the noise intensity. Also it has been demonstrated that the nonlinear system may be “linearized” by a strong noise.