An exact representation of the fermion dynamics in terms of Poisson   processes and its connection with Monte Carlo algorithms
  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. 
Matteo Beccaria, Carlo Presilla, Gian Fabrizio De Angelis, and   Giovanni Jona-Lasinio