  We investigate a reformulation of the dynamics of interacting fermion systems
in terms of a stochastic extension of Time Dependent Hartree-Fock equations.
The noise is found from a path-integral representation of the evolution
operator and allows to interpret the exact N-body state as a coherent average
over Slater determinants evolving under the random mean-fied. The full density
operator and the expectation value of any observable are then reconstructed
using pairs of stochastic uncorrelated wave functions. The imaginary time
propagation is also presented and gives a similar stochastic one-body scheme
which converges to the exact ground state without developing a sign problem. In
addition, the growth of statistical errors is examined to show that the
stochastic formulation never explode in a finite dimensional one-body space.
Finally, we consider initially correlated systems and present some numerical
implementations in exactly soluble models to analyse the precision and the
stability of the approach in practical cases.
