STATISTICal & A local limit theorem for hidden Markov chains

A local limit theorem is proved for partial sums of a hidden Markov chain, assuming lobal asymptotic normality for a related sum, a fairly weak mixing condition, and a non-lattice condition. The proof proceeds by a study of the conditional characteristic functions, the analysis of which relies heavily on a theorem from Breiman (1968). The paper concludes with a Cesaro type limit theorem for the joint distributions of the Markov chain and the partial sums