On L₁-weak ergodicity of markov processes

In the present paper we investigate the L₁-weak ergodicity of nonhomogeneous discrete Markov processes with general state spaces. Note that the L₁-weak ergodicity is weaker than well-known weak ergodicity. It was known a necessary and sufficient condition for such processes to satisfy the weak ergodicity. In this paper we provide a necessary and sufficient condition for nonhomogeneous discrete Markov processes to satisfy the L₁-weak ergodicity. Moreover, as an application of the main result, we provide more concrete examples of Markov processes which satisfy the L₁-weak ergodicity.