  Recently a generalized master equation was derived that extends the Lindblad
theory to highly non-Markovian quantum processes (H.-P. Breuer, Phys. Rev. A
\textbf{75}, 022103 (2007)). We perform a stochastic unravelling of this master
equation by considering $n$ random state vectors that satisfy the corresponding
stochastic differential equation for a piecewise deterministic process. As an
application we consider a two-state system randomly coupled to an environment
consisting of two energy bands with finite number of levels. Our numerical
results are compared to results obtained from the time-convolutionless (TCL)
projection operator method using correlated projection superoperators and the
exact solution of the Schr\"{o}dinger equation for this system.
