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Multiple hypotheses optimal testing for Markov chains and identification subject to the reliability criterion

Navaei L.

Journal of Mathematics and Applications

2010

Vol. 33

79-90

The problem of many (L > 2)hypotheses testing on distributions of a finite state Markov chain is studied. We apply large deviation techniques (LDT). It is demonstrated that this method of investigation in solving the problem of logarithmically asymptotically optimal (LAO) hypotheses testing is easier, compared with the procedure introduced by Haroutunian. The matrix of exponents [formula/wzór], of error probabilities of the LAO test [formula/wzór] is the probability to accept the hypothesis l, when the hypothesis m is true, is determined. Moreover, the identification of distributions for one object and two independent objects via simple homogeneous stationary Markov chains with finite number of states is discussed in the present paper.