Markov Chains

By: Revuz, DLanguage: English Series: North-Holland Mathematical Library ; 11Publication details: Amsterdam North-Holland 1984Description: xi, 374pISBN: 9780444864000 (HB)Subject(s): Markov Processes | Stochastic Processes | Probability | Mathematics
Contents:
1. Transition Probabilities Markov Chains 2. Potential Theory 3. Transcience and Recurrence 4. Pointwise Ergodic Theory 5. Transient Random Walks 6. Ergodic Theory of Harris Chains 7. Martin Boundary 8. Potential Theory for Harris Chains 9. Recurrent Random Walks 10. Construction of Markov Chains and Resolvents
Summary: This is the revised and augmented edition of a now classic book which is an introduction to sub-Markovian kernels on general measurable spaces and their associated homogeneous Markov chains. The first part, an expository text on the foundations of the subject, is intended for post-graduate students. A study of potential theory, the basic classification of chains according to their asymptotic behaviour and the celebrated Chacon-Ornstein theorem are examined in detail. The second part of the book is at a more advanced level and includes a treatment of random walks on general locally compact abelian groups. Further chapters develop renewal theory, an introduction to Martin boundary and the study of chains recurrent in the Harris sense. Finally, the last chapter deals with the construction of chains starting from a kernel satisfying some kind of maximum principle.
Item type: BOOKS List(s) this item appears in: New Arrivals (01 June 2024) | New Arrivals (01 June, 2024)
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519.21 REV (Browse shelf (Opens below)) Not for loan New Arrivals Displayed Till 15 May 2024 77923

Includes References (356-370)

1. Transition Probabilities Markov Chains
2. Potential Theory
3. Transcience and Recurrence
4. Pointwise Ergodic Theory
5. Transient Random Walks
6. Ergodic Theory of Harris Chains
7. Martin Boundary
8. Potential Theory for Harris Chains
9. Recurrent Random Walks
10. Construction of Markov Chains and Resolvents

This is the revised and augmented edition of a now classic book which is an introduction to sub-Markovian kernels on general measurable spaces and their associated homogeneous Markov chains. The first part, an expository text on the foundations of the subject, is intended for post-graduate students. A study of potential theory, the basic classification of chains according to their asymptotic behaviour and the celebrated Chacon-Ornstein theorem are examined in detail. The second part of the book is at a more advanced level and includes a treatment of random walks on general locally compact abelian groups. Further chapters develop renewal theory, an introduction to Martin boundary and the study of chains recurrent in the Harris sense. Finally, the last chapter deals with the construction of chains starting from a kernel satisfying some kind of maximum principle.

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