Drift conditions and invariant measures for Markov chains

We consider the classical Foster-Lyapunov condition for the existence of an invariant measure for a Markov chain when there are no continuity or irred ucibility assumptions. Provided a weak uniform countable additivity conditi on is satisfied, we show that there are a finite number of orthogonal invar iant measures under the usual drift criterion, and give conditions under wh ich the invariant measure is unique. The structure of these invariant measu res is also identified. These conditions are of particular value for a larg e class of non-linear time series models. (C) 2001 Elsevier Science B.V. Al l rights reserved.