Maximum likelihood estimator for hidden Markov models in continuous time

The paper studies large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain, observed in white noise. Using the method of weak convergence of likelihoods due to Ibragimov and Khasminskii (Statistical estimation, vol 16 of Applications of mathematics. Springer-Verlag, New York), consistency, asymptotic normality and convergence of moments are established for MLE under certain strong ergodicity assumptions on the chain. This article has been written during the author’s visit at Laboratoire de Statistique et Processus, Universite du Maine, France, supported by the Chateaubriand fellowship.