A theoretical framework for the description of fluctuating absorption coefficients of a guest molecule embedded in polymer or glass is presented. These fluctuations emerge in experiments with scans of laser frequency. A relation between theoretical expression for the time dependent single molecule absorption coefficient and the absorption coefficient measured in experiments with scanning laser frequency is discussed. The analysis is carried out for a guest molecule whose optical band consists of two well-resolved and poorly resolved optical lines. For well-resolved optical lines, measurement of auto- and cross-correlators is proposed. These correlators enable one to compare the fluctuating absorption coefficient with the time dependent absorption coefficient calculated theoretically with no adjustable parameters. For poorly resolved optical lines, the time dependent absorption coefficient enables one to calculate temporal line broadening of single molecule and to compare it with measured line broadening in time scale of seconds.