Stochastic nature of Galactic cosmic-ray sources

The precision measurements of the spectra cosmic ray nuclei and leptons in recent years have revealed existence multiple features, such as spectral break at $\sim 300$ GV rigidity seen by PAMELA AMS-02 more recently confirmed DAMPE CALET, softening H He 10$ TV reported DAMPE, confirming previous hints NUCLEON CREAM, a tiny change slope 40$ GeV electron spectrum, AMS-02, large $\sim$ TeV indirect (HESS, MAGIC VERITAS) direct (DAMPE, CALET) total (electrons+positrons) lepton spectrum. In all these cases, possibility has been suggested that features might reflect occasional presence local source, inducing noticeable reshaping average expected spectra. All proposals to face question how likely it is for source exist, we address here quantitative way. We study statistical properties random distribution sources space time, effect spiral structure our Galaxy both light (p He) (electrons positrons) different energy regions.