  We discuss two methods of an exact stochastic representation of the
non-Markovian quantum dynamics of open systems. The first method employs a pair
of stochastic product vectors in the total system's state space, while the
second method uses a pair of state vectors in the open system's state space and
a random operator acting on the state space of the environment. Both techniques
lead to an exact solution of the von Neumann equation for the density matrix of
the total system. Employing a spin star model describing a central spin coupled
to bath of surrounding spins, we perform Monte Carlo simulations for both
variants of the stochastic dynamics. In addition, we derive analytical
expression for the expectation values of the stochastic dynamics to obtain the
exact solution for the density matrix of the central spin.
