With the first edition out of print, we decided to arrange for republi- cation of Denumerable Markov Chains with additional bibliographic
material. The new edition contains a section Additional Notes that
indicates some of the developments in Markov chain theory over the
last ten years. As in the first edition and for the same reasons, we have
resisted the temptation to follow the theory in directions that deal with
uncountable state spaces or continuous time. A section entitled
Additional References complements the Additional Notes.
J. W. Pitman pointed out an error in Theorem 9-53 of the first
edition, which we have corrected. More detail about the correction
appears in the Additional Notes. Aside from this change, we have left
intact the text of the first eleven chapters.
The second edition contains a twelfth chapter, written by David
Griffeath, on Markov random fields. We are grateful to Ted Cox for
his help in preparing this material. Notes for the chapter appear in the
section Additional Notes.