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

Reduced equations of motion for quantum systems driven by diffusive Markov processes