so that transformed SDE then takes the form where superscript y indicates that Y y 0 = y , and EA utilises rejection sampling (von Neumann, 1951) to sample a skeleton of an SDE of interest. A skeleton is an exact (without discretisation error) sample of the SDE at a finite number of time points, which additionally contains information about the time interval of the path, [0 , t ], and path space information that ensures the sample path is almost surely constrained to some compact interval (Pollock, Johansen and Roberts, 2014). Denoting the target measure (the law of the SDE) as T$_{[0}$$_{,t}$$_{]}$ , skeletons are obtained via sampling from an equivalent proposal measure, P$_{[0}$$_{,t}$$_{]}$ , which is often taken to be standard Brownian motion. The probability of accepting proposed paths is proportional to the Radon-Nikod´ ym derivative of T$_{[0}$$_{,t}$$_{]}$ with respect to P$_{[0}$$_{,t}$$_{]}$ (Oksendal, 2000). In order to propose sample paths, we utilise the methodology developed in Chen and Huang (2013), which can be considered as a localised EA (LEA) approach. The localised approach partitions the simulation of a sample path by first fixing an interval around the initial value and then probabilistically samples an exit time and location for the proposed path. The simulated exit 11 α ( v ) = b (( η − $^{1}$( v )) σ (( η − $^{1}$( v )) − 1 2 σ $^{′}$( η − $^{1}$( v ) ) . d Y y s = α ( Y y s )d s + d W$_{s}$,