  We modify the path integral representation of exciton transport in open
quantum systems such that an exact description of the quantum fluctuations
around the classical evolution of the system is possible. As a consequence, the
time evolution of the system observables is obtained by calculating the average
of a stochastic difference equation which is weighted with a product of
pseudo-probability density functions. From the exact equation of motion one can
clearly identify the terms that are also present if we apply the truncated
Wigner approximation. This description of the problem is used as a basis for
the derivation of a new approximation, whose validity goes beyond the truncated
Wigner approximation. To demonstrate this we apply the formalism to a
donor-acceptor transport model.
