Irregular and Simulatable Functionals on Wiener Space

be locally Lipschitz. This occurs in particular when d — 1. In that case it is possible to construct almost sure and L approximations X'(u>) of X(u>) by approximating the Brownian path u> and using the continuity of the Ito mapping (see e.g. [6] [28] [21]). Actually, with or without the Frobenius assumption, direct discretization schemes X' can be constructed which converge in V and for some schemes almost surely, let us quote among a large literature on this subject [17] [7] [22] [19] [29] [11]. Now there are essentially two ways of using these approximations to compute numerically the expectation of the functional t'{J) = f{X(u>)) where / is a regular functional : 1. By L-approximation results, a functional Fe is first chosen, defined on a finite (eventually high) dimensional space, such that