Limit Theorems in Hidden Markov Models

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.

35 pages

References in corpus (5)

• Basic Properties of Strong Mixing Conditions. A Survey and Some Open Questions
• The Entropy of a Binary Hidden Markov Process
• Asymptotics of input-constrained binary symmetric channel capacity
• Taylor series expansions for the entropy rate of Hidden Markov Processes
• The Central Limit Theorem for uniformly strong mixing measures