In this work, a two step approach to model compound semiconductor epitaxy is presented. As first step, a Monte Carlo (MC) simulation of GaAs growth is developed, which may be understood as `numerical experiment'. To ensure the greatest possible agreement between MC simulations and real growth, all simulation parameters are determined unequivocally by comparison with experimental data taken during molecular beam epitaxy. On the other hand, a set of coupled rate equations for the densities of mobile species and of growth islands is formulated, which accounts for surface diffusion of Ga and As atoms as well as of GaAs molecules. With our self-consistent rate theory, we calculate average values of the densities of two-dimensional growth islands, mobile Ga atoms and GaAs molecules and compare these to MC simulation results. We find very good agreement indicating that the rate equations describe well the atomistic processes during growth.