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Data from the Voyager probes have provided us with the first measurement ofcosmic ray intensities at MeV energies, an energy range which had previouslynot been explored. Simple extrapolations of models that fit data at GeVenergies, e.g. from AMS-02, however, fail to reproduce the Voyager data in thatthe predicted intensities are too high. Oftentimes, this discrepancy isaddressed by adding a break to the source spectrum or the diffusion coefficientin an ad hoc fashion, with a convincing physical explanation yet to beprovided. Here, we argue that the discrete nature of cosmic ray sources, whichis usually ignored, is instead a more likely explanation. We model thedistribution of intensities expected from a statistical model of discretesources and show that its expectation value is not representative, but has aspectral shape different from that for a typical configuration of sources. TheVoyager proton and electron data are however compatible with the median of theintensity distribution. We stress that this model can explain the Voyager datawithout requiring any unphysical breaks.

Stochastic Fluctuations of Low-Energy Cosmic Rays and the Interpretation of Voyager Data