  We present a simple derivation of a Feynman-Kac type formula to study
fermionic systems. In this approach the real time or the imaginary time
dynamics is expressed in terms of the evolution of a collection of Poisson
processes. A computer implementation of this formula leads to a family of
algorithms parametrized by the values of the jump rates of the Poisson
processes. From these an optimal algorithm can be chosen which coincides with
the Green Function Monte Carlo method in the limit when the latter becomes
exact.
