Time evolution of averages in dynamical systems driven by noise

Abstract

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