  We treat several key stochastic equations for non-Markovian open quantum
system dynamics and present a formalism for finding solutions to them via
canonical perturbation theory, without making the Born-Markov or rotating wave
approximations (RWA). This includes master equations of the (asymptotically)
stationary, periodic, and time-nonlocal type. We provide proofs on the validity
and meaningfulness of the late-time perturbative master equation and on the
preservation of complete positivity despite a general lack of Lindblad form.
More specifically, we show how the algebraic generators satisfy the theorem of
Lindblad and Gorini, Kossakowski and Sudarshan, even though the dynamical
generators do not. These proofs ensure the mathematical viability and physical
soundness of solutions to non-Markovian processes. Within the same formalism we
also expand upon known results for non-Markovian corrections to the quantum
regression theorem. Several directions where these results can be usefully
applied to are also described, including the analysis of near-resonant systems
where the RWA is inapplicable and the calculation of the reduced equilibrium
state of open systems.
