Limiting Distribution and Ergodic Theorem

This lecture covers the concept of limiting distribution in Markov chains, defining it as the distribution to which a chain converges. It also explains the ergodic theorem, stating that an ergodic Markov chain admits a unique limiting and stationary distribution. The importance of aperiodicity in chains is highlighted, showing examples where it affects the existence of limiting distributions. The lecture concludes by discussing the ergodicity of chains and the implications for their stationary distributions.