The layout of this paper is as follows. In Section 2 we discuss the FKF, demonstrating how to represent local solutions of PDEs as expectations with respect to the law of complementary SDEs. In Section 3 we discuss how exact algorithms can be used to obtain unbiased local solutions to PDEs via exactly simulating from the complementary SDEs. In Section 4 we discuss how unbiased estimates can be obtained using discrete-time approximations of the complementary SDEs via debiasing. In Section 5 we give some nu- merical examples in order to compare the two approaches. In Section 6 we conclude and discuss future directions for research. The FKF relate solutions of a class of deterministic second order PDEs with expectations of initial and boundary functions with respect to the law of complementary SDEs. An introduction is available in Oksendal (2000), and covered in more detail in Pardoux and R˘ a¸scanu (2014). Consider the case where u ( x x, t ) ∈ C 2 , $^{1}$( R d × [0 , ∞ ) ) is the solution of a system described by the PDE with the initial condition u ( x x, 0) = f ( x ). This is known as the initial value problem. We assume that c ( x x, t ) is positive and bounded above, and that the coefficients in (1) satisfy the necessary conditions to ensure the existence 6 ∂u ∂t = d ∑ i,j =1 1 2 a$_{ij}$ ( x x, t ) ∂ $^{2}$u ∂x$_{i}$∂x$_{j}$ + d ∑ i =1 b$_{i}$ ( x x, t ) ∂u ∂x$_{i}$ − c ( x x, t ) u, x ∈ R $^{d}$, t > 0 . (1) 2. Feynman-Kac Formulae