  In this paper, we introduce a new approach to constructing unbiased
estimators when computing expectations of path functionals associated with
stochastic differential equations (SDEs). Our randomization idea is closely
related to multi-level Monte Carlo and provides a simple mechanism for
constructing a finite variance unbiased estimator with "square root convergence
rate" whenever one has available a scheme that produces strong error of order
greater than 1/2 for the path functional under consideration.
