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I'm trying to find out what is known about time-inhomogeneous ergodic Markov Chains where the transition matrix can vary over time. All textbooks and lecture notes I could find initially introduce Markov chains this way but then quickly restrict themselves to the time-homogeneous case where you have one transition matrix.

Obviously, in general such Markov chains might not converge to a unique stationary distribution, but I would be surprised if there isn't a large (sub)class of these chains where convergence is guaranteed. I'm particularly interested in theorems on the mixing time and convergence theorems that state when there exists a stationary distribution.

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    $\begingroup$ Isn't there a stationary convergence iff the transition matrix converge? $\endgroup$ – R B May 27 '14 at 11:16
  • $\begingroup$ Well, I was wondering whether this is true but couldn't find a reference. $\endgroup$ – markov-imitator May 28 '14 at 2:23
  • $\begingroup$ I'll try to post this on mathoverlow... $\endgroup$ – markov-imitator May 28 '14 at 7:37
  • $\begingroup$ Cross-posted to mathoverflow.net/questions/168398 . Next time, if you cross-post, please add links to the questions both ways. $\endgroup$ – Zsbán Ambrus May 28 '14 at 13:26

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