  The stability of solutions to evolution equations with respect to small
stochastic perturbations is considered. The stability of a stochastic dynamical
system is characterized by the local stability index. The limit of this index
with respect to infinite time describes the asymptotic stability of a
stochastic dynamical system. Another limit of the stability index is given by
the vanishing intensity of stochastic perturbations. A dynamical system is
stochastically unstable when these two limits do not commute with each other.
Several examples illustrate the thesis that there always exist such stochastic
perturbations which render a given dynamical system stochastically unstable.
The stochastic instability of quasi-isolated systems is responsible for the
irreversibility of time arrow.
