  It is shown that the exact dynamics of a composite quantum system can be
represented through a pair of product states which evolve according to a
Markovian random jump process. This representation is used to design a general
Monte Carlo wave function method that enables the stochastic treatment of the
full non-Markovian behavior of open quantum systems. Numerical simulations are
carried out which demonstrate that the method is applicable to open systems
strongly coupled to a bosonic reservoir, as well as to the interaction with a
spin bath. Full details of the simulation algorithms are given, together with
an investigation of the dynamics of fluctuations. Several potential
generalizations of the method are outlined.
