  We develop a statistical theory for the dynamics of non-aligning,
non-interacting self-propelled particles confined in a convex box in two
dimensions. We find that when the size of the box is small compared to the
persistence length of a particle's trajectory (strong confinement), the
steady-state density is zero in the bulk and proportional to the local
curvature on the boundary. Conversely, the theory may be used to construct the
box shape that yields any desired density distribution on the boundary. When
the curvature variations are small, we also predict the distribution of
orientations at the boundary and the exponential decay of pressure as a
function of box size recently observed in 3D simulations in a spherical box.
