  Light scattering from resonantly or nearly resonantly excited systems, known
as resonance fluorescence, has been gaining importance as a versatile tool for
investigating quantum states of matter and readout of quantum information,
recently including also the inherently noisy solid state systems. In this work
we develop a general theory of resonance fluorescence in the low excitation
limit on systems in which the transition energy is subject to noise for two
important classes of noise processes: white noise fluctuations that lead to
phase diffusion and an arbitrary stationary Markovian noise process on a finite
set of states. We apply the latter to the case of random telegraph noise and a
sum of an arbitrary number of identical random telegraph noise contributions.
We show that different classes of noise influence the RF spectrum in a
characteristic way. Hence, the RF spectrum carries information on the
characteristics of noise present in the physical system.
