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A local limit theorem for hidden Markov chains

✍ Scribed by Michael Maxwell; Michael Woodroofe

Book ID: 104302448
Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 252 KB
Volume: 32
Category: Article
ISSN: 0167-7152
DOI: 10.1016/s0167-7152(96)00064-8

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✦ Synopsis

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.

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