On sequential discrimination between close Markov chains

The appropriateness of the Wald-type logarithmic asymptotics for the mean length of sequential discrimination strategies between close alternatives has been already challenged in the well-known controversy over comparative performances of the asymptotically optimal Chernoffʹs discrimination strategies and ad hoc heuristic rules of Box and Hill in the seventies. tinue this discussion by showing a poor performance of the Wald-type asymptotic bounds for the mean length of asymptotically optimal sequential discrimination strategies between the simplest types of Markov chains by simulation. We propose some weak remedies against this disaster and some alternative asymptotic tools.