There is as of the writing of this (June 2006) no definitive treatise of the theory of KMC, but Fichthorn and Weinberg have discussed the theory for thermodynamic equilibrium KMC simulations in detail. A good introduction is given also by Art Voter, [1] and by A.P.J. Jansen, [2], and a recent review is (Chatterjee 2007) or (Chotia 2008). The justification of KMC as a coarse-graining of the Langevin dynamics using the quasi-stationary distribution approach has been developed by T. Lelièvre and collaborators.