Asymptotically optimal sequential discrimination between Markov chains

An asymptotic lower bound is derived involving a second additive term of order root /ln alpha/ as alpha --> 0 for the mean length of a sequential strategy 3 for discrimination between two statistical models for Markov chains. The parameter alpha is the maximal error probability of s. A sequential strategy is outlined attaining (or almost attaining) this asymptotic bound uniformly over the distributions of models including those from the indifference zone.