A stochastic model for simulating the growth processes during the low temperature molecular beam epitaxy of gallium arsenide is developed. The model includes the presence and dynamics of a weakly bound physisorbed state for arsenic. Three different kinetic models with a combination of surface kinetic processes such as incorporation of antisite arsenic, evaporation of antisite arsenic and incorporation of regular arsenic, were considered. The kinetic model which includes all three surface processes was the best model. The activation energy of 1.16eV for the evaporation of antisite arsenic from our model is in good agreement with theoretical estimates. At constant substrate temperature and growth rate, antisite arsenic concentration increases with arsenic flux for low fluxes and saturates for high fluxes. The critical arsenic flux at which the {dollar}As\sb{Ga}{dollar} concentration saturates increases with temperature and the {dollar}As\sb{Ga}{dollar} concentration saturates at lower values for higher temperatures. As the arsenic flux increases, the coverage of the physisorbed layer increases and at a critical flux the coverage saturates at its maximum value of unity and hence the concentration of {dollar}As\sb{Ga}{dollar} saturates. Lower {dollar}As\sb{Ga}{dollar} concentration results at higher temperature due to increased evaporation of {dollar}As\sb{Ga}.{dollar} The model predicted the existence of a critical temperature at which the maximum {dollar}As\sb{Ga}{dollar} concentration can be obtained. The experimental results confirmed the existence of this critical temperature. At a fixed value of arsenic flux the {dollar}As\sb{Ga}{dollar} concentration increases with decreasing temperature, to a critical temperature, and then decreases with further decrease in temperature. The critical temperature of 473{dollar}\sp\circ K{dollar} obtained from our model is in agreement with the experimental value. Above the critical temperature, evaporation kinetics dominates the surface processes, whereas below the critical temperature, the incorporation kinetics dominates. The {dollar}As\sb{Ga}{dollar} concentration increases with growth rate for low arsenic flux and decreases with growth rate for higher values. (Abstract shortened by UMI.).