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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.

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