  Bloch oscillations in nanoscale Josephson junctions with a Coulomb charging
energy comparable to the Josephson coupling energy are explored within the
context of a model previously considered by Geigenm\"uller and Sch\"on that
includes Zener tunneling and treats quasiparticle tunneling as an explicit
shot-noise process. The dynamics of the junction quasicharge are investigated
numerically using both Monte Carlo and ensemble approaches to calculate
voltage--current characteristics in the presence of microwaves. We examine in
detail the origin of harmonic and subharmonic Bloch steps at dc biases
$I=(n/m)2ef$ induced by microwaves of frequency $f$ and consider the optimum
parameters for the observation of harmonic ($m=1$) steps. We also demonstrate
that the GS model allows a detailed semi-quantitative fit to experimental
voltage--current characteristics previously obtained at the Chalmers University
of Technology, confirming and strengthening the interpretation of the observed
microwave-induced steps in terms of Bloch oscillations.
