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Questions about the properties of vector spaces and linear transformations, including linear systems in general.

9 votes
2 answers
882 views

Direct proof of unique invariant distribution for ergodic, positive-recurrent Markov chain

I posted the following question on MSE, feeling that it perhaps isn't research level mathematics, but didn't get any bites. So, I am crossposting here. The following ergodic theorem is well known. Er …
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  • 165
7 votes

Direct proof of unique invariant distribution for ergodic, positive-recurrent Markov chain

I came across another proof, by chance, for finite $I$. I saw this in old lecture notes by Peres on mixing times: Mixing for Markov Chains and Spin Systems (2005). Definition (Harmonic). A function $ …
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