A note on the ergodicity of Markov chains

Abstract

For an aperiodic, irreducible Markov chain with the non-negative integers as state space, a criterion for ergodicity is given. This criterion generalizes the criteria appearing in Foster (1953), Pakes (1969) and Marlin (1973), in the sense that any test function (Liapunov function) which satisfies their conditions also satisfies ours. Applications are presented through some examples.