This work focuses on the analysis of HIV infection dynamics during the initial stages of infection when the viral load is low and random fluctuations may have a significant effect on the dynamics of the disease. The ability of deterministic models to accurately describe the expected behavior of such processes is limited. Stochastic simulations, which are not hampered by this limitation, are used to determine the probability of successful infection in an average patient. Specifically, a stochastic model based on Gillespie's algorithm is derived and is employed to determine the sensitivity of HIV infection to different treatment strategies and the effect of latency in treatment initiation on virus clearance probability. The model is subsequently revised to include mutation in the virus genome and the response to treatment is analyzed.