Simple simulation of diffusion bridges with application to likelihood inference for diffusions

With a view to likelihood inference for discretely observed diffusion type models, we propose a simple method of simulating approximations to diffusion bridges. The method is applicable to all one-dimensional diffusion processes and has the advantage that simple simulation methods like the Euler … scheme can be applied to bridge simulation. Another advantage over other bridge simulation methods is that the proposed method works well when the diffusion bridge is defined in a long interval because the computational complexity of the method is linear in the length of the interval. In a simulation study we investigate the accuracy and efficiency of the new method and compare it to exact simulation methods. In the study the method provides a very good approximation to the distribution of a diffusion bridge for bridges that are likely to occur in applications to likelihood inference. To illustrate the usefulness of the new method, we present an EM-algorithm for a discretely observed diffusion process. We demonstrate how this estimation method simplifies for exponential families of diffusions and very briefly consider Bayesian inference.