Markov Chains
eBook - ePub

Markov Chains

  1. 373 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub

Markov Chains

Book details
Table of contents
Citations

About This Book

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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Information

Publisher
North Holland
Year
2008
ISBN
9780080880228
Topic
Mathématiques
Subtopic
Probabilités et statistiques

Table of contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. North-Holland Mathematical Library
  5. Front Matter
  6. Copyright page
  7. Preface to the First Edition
  8. Preface to the Second Edition
  9. Interdependence Guide
  10. Chapter 0: Preliminaries
  11. Chapter 1: Transition Probabilities. Markov Chains
  12. Chapter 2: Potential Theory
  13. Chapter 3: Transience and Recurrence
  14. Chapter 4: Pointwise Ergodic Theory
  15. Chapter 5: Transient Random Walks. Renewal Theory
  16. Chapter 6: Ergodic Theory of Harris Chains
  17. Chapter 7: Martin Boundary
  18. Chapter 8: Potential Theory for Harris Chains
  19. Chapter 9: Recurrent Random Walks
  20. Chapter 10: Construction of Markov Chains and Resolvents
  21. Notes and Comments
  22. References
  23. Index of Notation
  24. Index of Terms