  This paper concerns the use of the expectation-maximisation (EM) algorithm
for inference in partially observed diffusion processes. In this context, a
well known problem is that all except a few diffusion processes lack
closed-form expressions of the transition densities. Thus, in order to estimate
efficiently the EM intermediate quantity we construct, using novel techniques
for unbiased estimation of diffusion transition densities, a random weight
fixed-lag auxiliary particle smoother, which avoids the well known problem of
particle trajectory degeneracy in the smoothing mode. The estimator is
justified theoretically and demonstrated on a simulated example.
