is the strong order of the numerical discretization scheme. A lower variance estimator can be obtained by averaging over multiple, say N † , independent draws of u † ( xxx, t ), The expected computation time is proportional to ∑ ∞ j $_{=0}$2 $^{j}$P ( H ≥ j ). A comparison with (7) shows that the choice of distribution P ( H ) reflects a trade-off between lowering the variance of the estimator and computability. In Rhee and Glynn (2014) it is shown that if the strong order of the numer- ical scheme is greater than 0.5 then unbiased estimates can be obtained in finite expected computation time with square-root convergence rates. For unbounded SDEs the Milstein approximation has strong order 1, giving an effective way of obtaining FKF estimates for PDEs on infinite domains. How- ever, when the SDE is bounded, such as in the Dirichlet problem, the strong order is reduced to 0.5. This is a result of ignoring possible boundary inter- actions between discretely simulated points. With the slower rate of conver- gence, a finite variance estimator can be obtained by selecting P ( H ) so that P ( H ≥ j ) = 2 − jr for some r < 2 p , but computability may be an issue. The first example is a 1D advection-diffusion model. Consider the follow- ing parabolic PDE, which has previously been used to study finite difference 20 5.1. 1D Example 5. Numerical Examples u ‡ ( xxx, t ) = N † ∑ i =1 u † ( i $^{)}$( xxx, t ) .