See also http://math.stackexchange.com/questions/27514/nice-references-on-markov-chains-processes/27516#27516 – 2011-11-21
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I think it would be very helpful if you would write something about your background. Are you famliar with measure theoretic probability? Are you mainly interested in finite Markov chains? – 2012-05-11
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[27514] Nice references on Markov chains/processes?