The asymptotic redundancy of Bayes rules for Markov chains

We derive the asymptotics of the redundancy of Bayes rules for Markov chains of fixed order over a finite alphabet, extending the work of Barron and Clarke (1990) on independent and identically distributed (i.i.d.) sources. The asymptotics are derived when the actual source is the class of /spl phi/-mixing sources which strictly includes Markov chains. These results can be used to derive minimax asymptotic rates of convergence for universal codes when a Markov chain of fixed order is used as a model.