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Which is a good introductory book for Markov chains and Markov processes?

Thank you.

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    See also http://math.stackexchange.com/questions/27514/nice-references-on-markov-chains-processes/27516#275162011-11-21
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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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