  We investigate the stochastic dynamics of one sedimenting active Brownian
particle in three dimensions under the influence of gravity and passive
fluctuations in the translational and rotational motion. We present an
analytical solution of the Fokker--Planck equation for the stochastic process
which allows us to describe the dynamics of the active Brownian particle in
three dimensions. We address the time evolution of the monopole, the
polarization, and the steady-state solution. We also perform Brownian dynamics
simulations and study the effect of the activity of the particles on their
collective motion. These results qualitatively agree with our model. Finally,
we compare our results with experiments [J. Palacci \emph{et al.}, Phys. Rev.
Lett. \textbf{105}, 088304 (2010)] and find very good agreement.
