The radiative transport (or radiative migration) of electronic excitation energy in a molecular ensemble is analyzed from a stochastic point of view. This approach yields results considerably more general than those of previous treatments, where successive hops are (implicitly) assumed to be uncorrelated, while they constitute in fact a Markov process. The time evolution of the fluorescence intensity emitted by the molecular ensemble, in response to excitation by an external beam of linearly polarized and essentially monochromatic light is obtained. In contrast to the previous treatments, only known parameters are required. The time evolution of the fluorescence anisotropy is also obtained for the first time.