Undiased monte carlo estimators for functionals of weak solutions of stochastic diffretial equations

Abstract

A new numerical scheme for the evaluation of functional of weak solutions of Stochastic differential equations is considered. The scheme avoids the systematic error resulting from the discretisation in time of the stochastic differential equation. It is applicable to a wide class of functionals without the usual smoothness assumptions. The approach is based on the unbiased estimation of the transition density oft the solution process instead of the approximation of individual trajectories. Standard Monte Carlo techniques (the von Neumann-Ulam scheme) are developed and applied to the Kolmogorov backward equation. The new scheme includes the well known Euler scheme associated with some random correction term