approaches (Thongmoon and McKibbin, 2006), with initial and boundary conditions The complementary SDE for this system is which, when transformed using the Lamperti transform, becomes where y = x √$_{2}$$_{a}$ . The boundaries for the transformed SDE are 0 and 1 √$_{2}$$_{a}$ . Note that accepting proposed paths from this SDE does not require sampling from a Poisson process, owing to the fact that φ ( v ) is constant. Whilst this example is not fully demonstrative of the EA approach, it offers an analytical solution for comparison (Thongmoon and McKibbin, 2006). 21 dY y s = − b √$_{2}$$_{a}$ ds + dW$_{s}$, = − α ds + dW$_{s}$, dX x s = − b ds $_{+}$√$_{2}$$_{a dW}$$_{s}$$_{,}$ u ( x, 0) = 100 x, x ∈ [0 , 1] , u (0 , t ) = 0 , t ≥ 0 , u (1 , t ) = 100 , t ≥ 0 . ∂u ( x, t ) ∂t + b ∂u ( x, t ) ∂x = a ∂ $^{2}$u ( x, t ) ∂x 2 , t ≥ 0 , x ∈ [0 , 1] ,