A local limit theorem for hidden Markov chains

Michael Maxwell and Michael Woodroofe

Statistics & Probability Letters, 1997, vol. 32, issue 2, 125-131

Abstract: A local limit theorem is proved for partial sums of a hidden Markov chain, assuming global 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.

Keywords: Partial; sum; process; Stationary; sequence; Ergodic; theorem (search for similar items in EconPapers)
Date: 1997
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