Donsker’s delta functions and approximation of heat kernels by the time discretization methods

Introduction Time discretization approximation schemes for solutions of stochastic dierential equations have been studied by many people and are treated, e.g. in the book of Kloeden-Platen [Kl-Pl92]. Since heat kernels are the probability densities of the law of solutions, it might be worthwhile to ask if these approximation schemes provide a natural scheme of approximation for heat kenrnels. Purpose of this paper is to propose one of such schemes with a help of Malliavin calculus.