  The expansion of a stochastic Liouville equation for the coupled evolution of
a quantum system and an Ornstein-Uhlenbeck process into a hierarchy of coupled
differential equations is a useful technique that simplifies the simulation of
stochastically-driven quantum systems. We expand the applicability of this
technique by completely characterizing the class of diffusive Markov processes
for which a useful hierarchy of equations can be derived. The expansion of this
technique enables the examination of quantum systems driven by non-Gaussian
stochastic processes with bounded range. We present an application of this
extended technique by simulating Stark-tuned F\"orster resonance transfer in
Rydberg atoms with non-perturbative position fluctuations.

Quantum Physics;Chemical Physics