  We develop a Monte Carlo simulation method for computing stationary solutions
of the general-relativistic Vlasov equation describing a gas of non-colliding
particles. As specific examples, we select planar or spherically symmetric
accretion models on the Schwarzschild background spacetime. In all cases the
gas extends to infinity, which poses an additional difficulty in the Monte
Carlo approach. We discuss models with monoenergetic particles as well as
solutions obeying the Maxwell-J\"{u}ttner distribution at infinity. For all
models, exact expressions for the particle current density are known or can be
computed analytically. We demonstrate perfect agreement between exact
expressions for the particle current density and the results of our Monte Carlo
simulations.
