In studies of cosmic-ray propagation and diffuse continuum γ-ray emission from the Galaxy it has usually been assumed that the source function can be taken as smooth and time-independent, an approximation justified by the long residence time of cosmic-rays in the Galaxy. However, especially for electrons at high energies where energy losses are rapid, the effect of the stochastic nature of the sources becomes apparent and indeed has been invoked to explain the GeV excess in the diffuse emission observed by EGRET. In order to address this problem in detail a model with explicit time-dependence and a stochastic SNR population has been developed, which follows the propagation in three dimensions. The results indicate that although the inhomogeneities are large they are insufficient to easily explain the GeV excess. However the fluctuations should show up in the gamma-ray distribution at high energies and this should be observable with GLAST. We also show that estimates of the TeV continuum emission from the ...
