State space models is a very general class of time series models
capable of modelling dependent observations in a natural and interpretable way.
Inference in such models has been studied by Bickel, Ritov and Rydén,
who consider hidden Markov models, which are special kinds of state space
models, and prove that the maximum likelihood estimator is asymptotically
normal under mild regularity conditions. In this paper we generalize the
results of Bickel, Ritov and Rydén to state space models, where the
latent process is a continuous state Markov chain satisfying regularity
conditions, which are fulfilled if the latent process takes values in a compact
space.