A New Condition for Ergodicity of Markov Chains with a General State Space

The paper suggests a new condition, specifically a two-set decomposition of a Markov chain, guaranteeing the existence of a unique stationary distribution of the Markov chain with a general state space. This condition turns out to be sufficient for ergodicity of the Markov chain under the Harris recurrent condition. A comparison of the suggested condition with the known Doeblin condition and $\phi$-irreduciblity condition is given, and a concrete illustrative example is provided.