Multiple objects: error exponents in hypotheses testing and identification
Information Theory, Combinatorics, and Search Theory
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Let{X_{n}} n geq 1be 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.