Consistency of MLE in partially observed diffusion models on a torus

In this paper, we consider a general partially observed diffusion model with periodic coefficients and with non-degenerate diffusion component. The coefficients of such a model depend on an unknown (static and deterministic) parameter which needs to be estimated based on the observed component of the diffusion process. We show that, given enough regularity of the diffusion coefficients, a maximum likelihood estimator of the unknown parameter converges to the true parameter value as the sample size grows to infinity.