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tance probability proportional to (5). This requires calculating an upper bound for exp( A ( v )), and upper and lower bounds for φ ( v ) over the current interval. For the Dirichlet problem it is possible to obtain bounds over the entire domain, which can then be applied to every interval. Whether this is a more computationally efficient approach than evaluating tighter bounds in each iteration will be problem dependent. Whilst it is not possible to com- pute the acceptance probability directly as it requires the full sample path, an unbiased acceptance probability can be obtained using Poisson thinning (Lewis and Shedler, 1979), which requires only a finite dimensional repre- sentation of the sample path (Beskos, Papaspiliopoulos and Roberts, 2006a; Chen and Huang, 2013). 

Accepted simulations from EA can be used to obtain Monte Carlo es- timates of the FKF by using the inverse of the Lamperti transform. Since the function c ( x, t ) is required to be bounded, say by L$_{c}$ and M$_{c}$ , the path weighting term in (3) and (4) can also be estimated using Poisson thinning. A naive Monte Carlo estimate is then given by 

where each ˆ u ( i ) are of the form 

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<img src='content_image/322840.jpg'>

