On the Complexity of Computing Quadrature Formulas for SDEs

Abstract

We survey recent results on the constructive approximation of the distribution of the solution of an SDE by probability measures with finite support, i.e., by quadrature formulas with positive weights summing up to one. Here we either consider the distribution on the path space or a marginal distribution on the state space. We provide asymptotic results on the N -th minimal error of deterministic and randomized algorithms, which is the smallest error that can be achieved by any such algorithm not exceeding the cost bound N .