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 (t
ransitions over potential barriers) the time evolution of the mean coordina
te 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 ''linearize
d'' by a strong noise. (C) 1999 Published by Elsevier Science B.V. All righ
ts reserved.