  A stochastic approach to the quantum dynamics randomly modulated in time by a
discrete state non-Markovian noise, which possesses an arbitrary
non-exponential distribution of the residence times, is developed. The formally
exact expression for the Laplace-transformed quantum propagator averaged over
the stationary realizations of such N-state non-Markovian noise is obtained.
The theory possesses a wide range of applications. It includes some previous
Markovian and non-Markovian theories as particular cases. In the context of
stochastic theory of spectral line shape and relaxation, the developed approach
presents a non-Markovian generalization of the Kubo-Anderson theory of sudden
modulation. In particular, the exact analytical expression is derived for the
spectral line shape of optical transitions described by a Kubo-oscillator with
randomly modulated frequency which undergoes jump-like non-Markovian
fluctuations in time.
