Invariant Measures: Properties and Applications

This lecture introduces the concept of invariant measures in the context of Markov chains, focusing on their properties and applications. The instructor explains how invariant measures differ from invariant distributions and discusses their significance in continuous-time processes. The lecture covers the existence and uniqueness of invariant measures, along with their role in analyzing irreducible recurrent Markov chains. Key topics include the proof of existence, temporal shifts, and the ergodic theorem.