  In this paper we present a quantum stochastic model for spectroscopic
line-shapes in the presence of a co-evolving and non-stationary background
population of excitations. Starting from a field theory description for
interacting bosonic excitons, we derive a reduced model whereby optical
excitons are coupled to an incoherent background via scattering as mediated by
their screened Coulomb coupling. The Heisenberg equations of motion for the
optical excitons are then driven by an auxiliary stochastic population
variable, which we take to be the solution of an Ornstein-Uhlenbeck process.
It\^o's Lemma then allows us to easily construct and evaluate correlation
functions and response functions. Focusing on the linear response, we compare
our model to the classic Anderson-Kubo model. While similar in motivation,
there are profound differences in the predicted lineshapes, notably in terms of
asymmetry, and variation with increasing background population.
