KMT Theory Applied to Approximations of SDE

The dyadic method of Komlós, Major and Tusnády is a powerful way of constructing simultaneous normal approximations to a sequence of partial sums of i.i.d. random variables. We use a version of this KMT method to obtain order 1 approximation in a Vaserstein metric to solutions of vector SDEs under a mild non-degeneracy condition using an easily implemented numerical scheme.