  We constructed the representation of contextual probabilistic dynamics in the
complex Hilbert space. Thus dynamics of the wave function can be considered as
Hilbert space projections of realistic dynamics in a ``prespace''. The basic
condition for representing of the prespace-dynamics is the law of statistical
conservation of energy -- conservation of probabilities. Construction of the
dynamical representation is an important step in the development of contextual
statistical viewpoint to quantum processes. But the contextual statistical
model is essentially more general than the quantum one. Therefore in general
the Hilbert space projection of the ``prespace'' dynamics can be nonlinear and
even irreversible (but it is always unitary). There were found conditions of
linearity and reversibility of the Hilbert space dynamical projection. We also
found conditions for the conventional Schroedinger dynamics (including
time-dependent Hamiltonians). We remark that in general even the Schroedinger
dynamics is based just on the statistical conservation of energy; for
individual systems the law of conservation of energy can be violated (at least
in our theoretical model).
