Testing hypotheses for Markov chains when the parameter space is finite

In Chernoff [2], a procedure was presented for the sequential design of experiments where the problem was one of testing a hypothesis. When there were only a finite number of states of nature and a finite number of available experiments, the procedure was shown to be " asymptotically optimal" as the cost of sampling approached zero. An analogous procedure can be applied to the problem of testing a hypothesis with respect to a Markov process, and this procedure will also be shown to be " asymptotically optimal".