Ergodic Markov Chain

Definition

The HMC $\{X_t\}$ that satisfies the following conditions is an ergodic Markov chain

• has finite states
• irreducible
• aperiodic

The HMC $\{X_t\}$ that satisfies the following conditions is an ergodic Markov chain

• irreducible
• Positive recurrent
• aperiodic