This paper provides closed-form expansions for the log-likelihood function of multivariate diffusions sampled at discrete time intervals. The coefficients of the expansion are calculated explicitly by exploiting the special structure afforded by the diffusion model. Examples of interest in financial statistics and Monte Carlo evidence are included, along with the convergence of the expansion to the true likelihood function.
"Closed-form likelihood expansions for multivariate diffusions." Ann. Statist. 36 (2) 906 - 937, April 2008. https://doi.org/10.1214/009053607000000622