Denumerable Markov Chains: with a chapter of Markov Random Fields by David Griffeath

✍ Scribed by John G. Kemeny, J. Laurie Snell, Anthony W. Knapp (auth.)

• Publisher: Springer-Verlag New York
• Year: 1976
• Tongue: English
• Leaves: 495
• Series: Graduate Texts in Mathematics 40
• Edition: 2
• Category: Library

✦ Synopsis

With the first edition out of print, we decided to arrange for republi­ cation of Denumerrible Markov Ohains 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. J.G.K., J.L.S., A.W.K.

✦ Table of Contents

Front Matter....Pages i-xii
Prerequisites From Analysis....Pages 1-39
Stochastic Processes....Pages 40-57
Martingales....Pages 58-78
Properties of Markov Chains....Pages 79-105
Transient Chains....Pages 106-129
Recurrent Chains....Pages 130-165
Introduction to Potential Theory....Pages 166-190
Transient Potential Theory....Pages 191-240
Recurrent Potential Theory....Pages 241-322
Transient Boundary Theory....Pages 323-400
Recurrent Boundary Theory....Pages 401-424
Introduction to Random Fields....Pages 425-458
Back Matter....Pages 459-484

✦ Subjects

Analysis