  The exact dynamics of a system coupled to an environment can be described by
an integro-differential stochastic equation of its reduced density. The
influence of the environment is incorporated through a mean-field which is both
stochastic and non-local in time and where the standard two-times correlation
functions of the environment appear naturally. Since no approximation is made,
the presented theory incorporates exactly dissipative and non-Markovian
effects. Applications to the spin-boson model coupled to a heat-bath with
various coupling regimes and temperature show that the presented stochastic
theory can be a valuable tool to simulate exactly the dynamics of open quantum
systems. Links with stochastic Schroedinger equation method and possible
extensions to "imaginary time" propagation are discussed.
