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 dictated by probabilistic features of the acting noise. Contrary to the standard approaches, we do not assume a Markov character of the environmental influence. Instead, the probabilistic properties of a jump to an environment state depend on the residence time in the preceding state. Our method is based on the explicit construction of all possible spectral trajectories and their corresponding probabilities. It allows for a detailed calculation of the time-dependent spectral features (absorption and fluorescence).