Single molecular unit embedded in a local environment is influenced by
the time-dependent stochastic microfield created by the neighbouring
host molecules. The spectral behaviour of the impurity molecule is dic
tated by probabilistic features of the acting noise. Contrary to the s
tandard approaches, we do not assume a Markov character of the environ
mental influence. Instead, the probabilistic properties of a jump to a
n environment state depend on the residence time in the preceding stat
e. Our method is based on the explicit construction of all possible sp
ectral trajectories and their corresponding probabilities. It allows f
or a detailed calculation of the time-dependent spectral features (abs
orption and fluorescence).