The process of auto-ignition in a non-premixed, homogeneous and isotropic turbulent medium is considered. The governing pdf transport equation is simulated via a Monte Carlo method. It is found that the pdf evolution depends on the relative magnitudes of two time scales, namely, that of turbulent mixing and of chemical reaction. Calculations made for a wide range of these time scales show that at least four different regimes of auto-ignition may be identified. These are classified into premixed and non-premixed type, and are located on a Damkohler number diagram.