Asymptotics of the maximum likelihood estimator for general hidden Markov models

In this paper, we consider the consistency and asymptotic normality of the maximum likelihood estimator for a possibly non-stationary hidden Markov model where the hidden state space is a separable and compact space not necessarily finite, and both the transition kernel of the hidden chain and the conditional distribution of the observations depend on a parameter theta. For identifiable models, consistency and asymptotic normality of the maximum likelihood estimator are shown to follow from exponential memorylessness properties of the state prediction filter and geometric ergodicity of suitably extended Markov chains.