  High-energy cosmic-ray electrons reveal some remarkable spectral features,
the most noteworthy of which is the rise in the positron fraction above 10~GeV.
Due to strong energy loss during propagation, these particles can reach Earth
only from nearby sources. Yet, the exact nature of these sources, which most
likely manifest themselves in the observed anomalies, remains elusive. The many
explanations put forward to resolve this case range from standard astrophysics
to exotic physics. In this paper, we discuss the possible astrophysical origin
of high-energy cosmic-ray electrons through a fully three-dimensional
time-dependent Monte Carlo simulation. This approach, which takes advantage of
the intrinsic random nature of cosmic-ray diffusive propagation, provides
valuable information on the electron-by-electron fluctuations, making it
particularly suitable for analyzing in depth the single-source scenario.
