A semi-classical approach to the study of the evolution of anyonic excitations–elementary particles with fractional statistics, complementing bosons and fermions–is through the Boltzmann equation for anyons. This work reviews a discretized version–a system of partial differential equations–of such a quantum equation. Trend to equilibrium is studied for a planar stationary system, as well as the spatially homogeneous system. Essential properties of the linearized operator are proven, implying that results for general steady half-space problems for the discrete Boltzmann equation in a slab geometry can be applied.