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Markov chains /
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....
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam ; New York :
North-Holland,
1984.
|
| Edición: | Rev. ed. |
| Colección: | North-Holland mathematical library ;
v. 11. |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo Texto completo |
MARC
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| 072 | 7 | |a MAT |x 029040 |2 bisacsh | |
| 082 | 0 | 4 | |a 519.2/33 |2 22 |
| 100 | 1 | |a Revuz, D. | |
| 245 | 1 | 0 | |a Markov chains / |c D. Revuz. |
| 250 | |a Rev. ed. | ||
| 260 | |a Amsterdam ; |a New York : |b North-Holland, |c 1984. | ||
| 300 | |a 1 online resource (xi, 374 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a North-Holland mathematical library ; |v v. 11 | |
| 520 | |a 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. | ||
| 504 | |a Includes bibliographical references (pages 356-370) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Front Cover; Markov Chains; Copyright Page; PREFACE TO FIRST EDITION; PREFACE TO SECOND EDITION; INTERDEPENDENCE GUIDE; CONTENTS; CHAPTER 0. PRELIMINARIES; 1. Notation; 2. Martingales; 3. The monotone class theorem; 4. Topological spaces and groups; CHAPTER 1. TRANSITION PROBABILITIES. MARKOV CHAINS; 1. Kernels. Transition probabilities; 2. Homogeneous Markov chains; 3. Stopping times. Strong Markov property; 4. Random walks on groups and homogeneous spaces; 5. Analytical properties of integral kernels; CHAPTER 2. POTENTIAL THEORY; 1. Superharmonic functions and the maximum principle | |
| 505 | 8 | |a 2. Reduced functions and balayage3. Equilibrium, invariant events and transient sets; 4. Invariant and excessive measures; 5. Randomized stopping times and filling scheme; 6. Resolvents; CHAPTER 3. TRANSIENCE AND RECURRENCE; 1. Discrete Markov chains; 2. Irreducible chains and Harris chains; 3. Topological recurrence of random walks; 4. Recurrence criteria for random walks and applications; CHAPTER 4. POINTWISE ERGODIC THEORY; 1. Preliminaries; 2. Maximal ergodic lemma. Hopf's decomposition; 3. The Chacon-Ornstein theorem for conservative contractions; 4. Applications to Harris chains | |
| 505 | 8 | |a 5. Brunel's lemma and the general Chacon-Ornstein theorem6. Subadditive ergodic theory; CHAPTER 5. TRANSIENT RANDOM WALKS. RENEWAL THEORY; 1. The theorem of Choquet and Deny; 2. General lemmas; 3. The renewal theorem for the groups R and Z; 4. The renewal theorem; 5. Refinements and applications; CHAPTER 6. ERGODIC THEORY OF HARRIS CHAINS; 1. The zero-two laws; 2. Cyclic classes and limit theorems for Harris chains; 3. Quasi-compact transition probabilities and strong ergodic theorem; 4. Special functions; 5. Potential kernels; 6. The ratio-limit theorem; CHAPTER 7. MARTIN BOUNDARY | |
| 505 | 8 | |a 1. Regular functions2. Convergence to the boundary; 3. Integral representation of harmonic functions; CHAPTER 8. POTENTIAL THEORY FOR HARRIS CHAINS; 1. Harris chains and duality; 2. Equilibrium, balayage and maximum principles; 3. Normal chains; 4. Feller chains and recurrent boundary theory; CHAPTER 9. RECURRENT RANDOM WALKS; 1. Preliminaries; 2. Normality and potential kernels; 3. Martin boundary; 4. Renewal theory; CHAPTER 10. CONSTRUCTION OF MARKOV CHAINS AND RESOLVENTS; 1. Preliminaries and bounded kernels; 2. The reinforced principle. Construction of transient Markov chains | |
| 505 | 8 | |a 3. The semi-complete maximum principleNOTES AND COMMENTS; REFERENCES; INDEX OF NOTATION; INDEX OF TERMS | |
| 546 | |a English. | ||
| 650 | 0 | |a Markov processes. | |
| 650 | 2 | |a Markov Chains |0 (DNLM)D008390 | |
| 650 | 6 | |a Processus de Markov. |0 (CaQQLa)201-0024070 | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x Stochastic Processes. |2 bisacsh | |
| 650 | 7 | |a Markov processes |2 fast |0 (OCoLC)fst01010347 | |
| 650 | 7 | |a Markov, processus de. |2 ram | |
| 653 | |a Markov chains | ||
| 776 | 0 | 8 | |i Print version: |a Revuz, D. |t Markov chains. |b Rev. ed. |d Amsterdam ; New York : North-Holland, 1984 |z 0444864008 |z 9780444864000 |w (DLC) 83011586 |w (OCoLC)9622061 |
| 830 | 0 | |a North-Holland mathematical library ; |v v. 11. | |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/book/9780444864000 |z Texto completo |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/publication?issn=09246509&volume=11 |z Texto completo |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/bookseries/09246509/11 |z Texto completo |