  Within a density matrix approach for nuclear many--body system, it is derived
non--Markovian Langevin equations of motion for nuclear collective parameters,
where memory effects are defined by memory time. The developed stochastic
approach is applied to study both the nuclear descent from fission barrier to a
scission point and thermal diffusive overcoming of the barrier. The present
paper is partly a review of our results obtained earlier and contains new
results on the non--Markovian generalization of Kramers' theory of escape rate
and on time features of the collective dynamics in the presence of periodic
external modulation.
