advancements in exact simulation of SDEs and debiasing methods, provides a way to obtain unbiased estimates of local solutions to a class of second order parabolic PDEs. The practice of using finite difference or finite element methods to solve such problems leads to discretisation errors, and requires obtaining global solutions. The FKF approach presented here therefore seems to be a more efficient approach in situations in which only local solutions are required. A well known example is the Bayesian inverse problem (Stuart, 2010), in which local solutions are required in order to obtain likelihood estimates given a set of data. The fact that the estimates presented here are unbiased means that it is possible to design exact Monte Carlo algorithms to sample from the posterior distributions, as shown in Herbei and Berliner (2014). Even in situations where data are abundant, it is trivial to implement the FKF approach in parallel, limiting the computational expense to the single most expensive estimate. Exact simulation methods seem to outperform debiasing approaches, which suffer from both large estimator variance and computational expense when the domain of the PDE is bounded. However, current restrictions on ex- act algorithms, particularly in multiple dimensions, mean that they can not be used for a large number of interesting models. The reasons for this are twofold: in multiple dimensions it is not typically possible to transform an SDE to have unit diffusion, and the drift function must be of a suitable form to bound the Raydon-Nikod´ ym derivative. It seems unlikely that these issues will be overcome in the current class of EA algorithms. On the other hand, if 26