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Large deviations, hypotheses testing, and source coding for finite Markov chains

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1 Author(s)

Let {X_{n}} n \geq 1 be a finite Markov chain with transition probability matrix of strictly positive entries. A large deviation theorem is proved for the empirical transition count matrix and is used to get asymptotically optimal critical regions for testing simple hypotheses about the transition matrix. As a corollary, the error exponent in the source coding theorem for {X_{n}} is obtained. These results generalize the corresponding results for the independent and identically distributed case.

Published in:

IEEE Transactions on Information Theory  (Volume:31 ,  Issue: 3 )