Sequential estimation of the parameter of a Markov chain

The paper deals with the problem of sequential estimation from dependent observations. For this case, an inequality of the Wolfowitz type is derived and its asymptotical behaviour is investigated. Sufficient conditions are given for Markov observations under which the bound in the Wolfowitz type inequality for sequential estimation is asymptotically equal to that in the non-sequential case. These results are illustrated by examples in which sequential estimation does not improve asymptotically the estimates.