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In the first part of this work [4] we have studied the approximation problem of IEf(X T ) by IEf(X n T ), where (X t ) is the solution of a stochastic differential equation, (X n t ) is defined by the Euler discretization scheme with step T n , and f(\Delta) is a given function, only supposed measurable and bounded. We have proven that the discretization error can be expanded in terms of powers of 1 n under a nondegeneracy condition of H#rmander type for the infinitesimal generator of (X t )....

The Law of the Euler Scheme for Stochastic Differential Equations: II. Convergence Rate of the Density