  A stochastic representation of the dynamics of open quantum systems, suitable
for non-perturbative system-reservoir interaction, non-Markovian effects and
arbitrarily driven systems is presented. It includes the case of driving on
timescales comparable to or shorter than the reservoir correlation time, a
notoriously difficult but relevant case in the context of quantum information
processing and quantum thermodynamics. A previous stochastic approach is
re-formulated for the case of finite reservoir correlation and response times,
resulting in a numerical simulation strategy exceeding previous ones by orders
of magnitude in efficiency. Although the approach is based on a memory
formalism, the dynamical equations propagated in the simulations are
time-local. This leaves a wide range of choices in selecting the system to be
studied and the numerical method used for propagation. For a series of tests,
the dynamics of the spin-boson system is computed in various settings including
strong external driving and Landau-Zener transitions.
