Question: A foundational fact that is extremely useful in the study of Markov Chains, is the fact that every finite state Markov chain has an invariant

A foundational fact that is extremely useful in the study of Markov Chains, is the fact that every finite state Markov chain has an invariant probability distribution. It is beyond the scope of this class (and certainly this homework!) to discuss this any further; however, as you will see, we have already developed enough tools to actually prove this, using optimization and duality

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