Redundancy of Universal Coding of Arbitrary Markov Sources

It is given that letters of an input alphabet are generated by a certain $s$-connected Markov source. A coding is called universal if its redundancy tends to zero for any source. The asymptotic behavior of the redundancy of such a coding is determined for the class of $s$-connected Markov sources. An upper bound has been obtained for it by Yu. M. Shtar'kov. For $s=0$ the results concur with the results of K. E. Krichevskii for Bernoulli sources.