A Monte Carlo method was introduced for maximum-likelihood inference in the context of discretely observed diffusion processes. The method gave unbiased and continuous estimators of the likelihood function for a family of diffusion models, and its performance in numerical examples was computationally efficient. It exploited a new technique for the exact simulation of diffusion, and involved no discretization errors. It was shown that, under regularity conditions, the Monte Carlo maximum likelihood estimate converged to the true maximum likelihood estimate. For data-sizes, n→∞, it was shown that the number of Monte Carlo iterations should be tuned as O(n½), and the consistency of the Monte Carlo maximum likelihood estimate, as an approach to the true parameter value, was demonstrated.

Monte Carlo Maximum Likelihood Estimation for Discretely Observed Diffusion Processes. A.Beskos, O.Papaspiliopoulos, G.Roberts: Annals of Statistics, 2009, 37[1], 223-45