Limit Theorems in Hidden Markov Models

2011/02/02 by Guangyue Han, Han, Guangyue
Computer Science · Mathematics · #60F05 #60F15 #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT #msc:60F05 #msc:60F15

paper · pdf · doi:10.48550/arxiv.1102.0365

35 pages

arxiv created 2012/04/12 · arxiv updated 2012/04/13

Abstract

In this paper, under mild assumptions, we derive a law of large numbers, a central limit theorem with an error estimate, an almost sure invariance principle and a variant of Chernoff bound in finite-state hidden Markov models. These limit theorems are of interest in certain ares in statistics and information theory. Particularly, we apply the limit theorems to derive the rate of convergence of the maximum likelihood estimator in finite-state hidden Markov models.

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