Markov Chains:
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham
Springer
[2018]
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| Schriftenreihe: | Springer series in operations research and financial engineering
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xviii, 757 Seiten Diagramme |
| ISBN: | 9783319977034 |
Internformat
MARC
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| 245 | 1 | 0 | |a Markov Chains |c Randal Douc ; Eric Moulines ; Pierre Priouret ; Philippe Soulier |
| 264 | 1 | |a Cham |b Springer |c [2018] | |
| 300 | |a xviii, 757 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer series in operations research and financial engineering | |
| 650 | 4 | |a Probability Theory and Stochastic Processes | |
| 650 | 4 | |a Distribution (Probability theory | |
| 650 | 0 | 7 | |a Markov-Kette |0 (DE-588)4037612-6 |2 gnd |9 rswk-swf |
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| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Moulines, Eric |d 1963- |0 (DE-588)1050741625 |4 aut | |
| 700 | 1 | |a Priouret, Pierre |d 1939- |0 (DE-588)173702538 |4 aut | |
| 700 | 1 | |a Soulier, Philippe |0 (DE-588)1178465055 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-319-97704-1 |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-030829087 | |
Datensatz im Suchindex
| _version_ | 1826181941591801856 |
|---|---|
| adam_text |
Contents Part I Foundations 1 Markov Chains: Basic Definitions. 1.1 Markov Chains. 1.2 Kernels. 1.3 Homogeneous Markov Chains. 1.4 Invariant Measures and Stationarity. 1.5 Reversibility. 1.6 Markov Kernels on Lf(ī). 1.7 Exercises. 1.8 Bibliographical Notes. 3 3 6 12 16 18 20 21 25 2 Examples of Markov Chains. 2.1 Random Iterative Functions. 2.2 Observation-Driven Models. 2.3 Markov Chain Monte Carlo Algorithms . 2.4 Exercises. 2.5 Bibliographical Notes. 27 27 35 38 49 51 3 Stopping Times and the Strong Markov Property. 3.1 The Canonical
Chain. 3.2 Stopping Times. 3.3 The Strong Markov Property. 3.4 First-Entrance, Last-Exit Decomposition. 3.5 Accessible and Attractive Sets. 3.6 Return Times and Invariant Measures. 3.7 Exercises. 3.8 Bibliographical Notes. 53 54 58 60 64 66 67 73 74 xiii
4 5 XV Contents Martingales, Harmonic Functions and Poisson-Dirichlet Problems. 4.1 Harmonic and Superharmonic Functions. 4.2 The Potential Kemel. 4.3 The Comparison Theorem. 4.4 The Dirichlet and Poisson Problems. 4.5 Time-Inhomogeneous Poisson-Dirichlet Problems. 4.6 Exercises. 4.7 Bibliographical Notes. Ergodic Theory for Markov Chains. 5.1 Dynamical Systems. 5.2 Markov Chain Ergodicity. 5.3 Exercises. 5.4 Bibliographical Notes. Contents 9 75 75 77 81 85 88 89 95 »jtøWtr*· xiv Part II 6 7 8 Irreducible Chains: Basics 11 Splitting Construction and Invariant Measures 11.1 The Splitting Construction. 11.2 Existence of Invariant Measures.
11.3 Convergence in Total Variation tothe Stationary Distribution. 11.4 Geometric Convergence in Total Variation Distance . 11.5 Exercises. 11.6 Bibliographical Notes. 1 l.A Another Proof of the Convergenceof Harris Recurrent Kemels. 241 241 247 Feller and f-Kernete. 12.1 Feller Kernels. 12.2 Г-Kemels . 12.3 Existence of an Invariant Probability. 12.4 Topological Recurrence. 12.5 Exercises. 12.6 Bibliographical Notes. 12.A Linear Control Systems. 265 265 270 274 277 279 285 285 ļ į ·. Atomic Chains. П9 6.1
Atoms. 119 6.2 Recurrence and Transience. 121 6.3 Period of an Atom. 126 6.4 Subinvariant and Invariant Measures. 128 6.5 Independence of the Excursions. 134 6.6 Ratio Limit Theorems . 135 6.7 The Central Limit Theorem. 137 6.8 Exercises. 140 6.9 Bibliographical Notes. 144 Markov Chains on aDiscrete StateSpace. 7.1 Irreducibility, Recurrence, and Transience. 7.2 Invariant Measures, Positive and Null Recurrence. 7.3 Communication. 7.4 Period. 7.5 Drift Conditions for Recurrence and Transience. 7.6 Convergence to the Invariant Probability. 7.7 Exercises. 7.8
Bibliographical Notes. 145 145 146 148 150 151 154 164 Convergence of Atomic MarkovChains. 8.1 Discrete-Time Renewal Theory. 8.2 Renewal Theory and Atomic Markov Chains. 8.3 Coupling Inequalities for Atomic Markov Chains . 8.4 Exercises. 8.5 Bibliographical Notes. 165 165 175 180 187 189 159 211 215 215 Transience, Recurrence, and Harris Recurrence 221 10.1 Recurrence and Transience. 221 10.2 Harris Recurrence. 228 10.3 Exercises. 236 10.4 Bibliographical Notes. 239 •I įj 191 ^ 194 201 10 97 97 104 Ill 115 Small Sets, Irreducibility, and Aperiodicity 9.1 Small Sets. 9.2 Irreducibility. 9.3 Periodicity and Aperiodicity. 9.4 Petite
Sets. 9.5 Exercises. 9.6 Bibliographical Notes. 9.A Proof of Theorem 9.2.6. 12 Part III 13 251 253 258 259 259 Irreducible Chains: Advanced Topics Rates 13.1 13.2 13.3 13.4 13.5 13.6 of Convergence for Atomic Markov Chains. Subgeometric Sequences. Coupling Inequalities for Atomic Markov Chains . Rates of Convergence in Total Variation Distance. Rates of Convergence in /-Norm. Exercises. Bibliographical Notes. 289 289 291 303 305 311 312
XVI 14 15 16 17 18 19 Contents Geometric Recurrence and Regularity. 14.1 /-Geometric Recurrence and Drift Conditions. 14.2 /-Geometric Regularity. 14.3 /֊Geometric Regularity of the Skeletons. 14.4 /-Geometric Regularity of the Split Kernel. 14.5 Exercises. 14.6 Bibliographical Notes. 313 313 321 327 332 334 337 Geometric Rates of Convergence. 15.1 Geometric Ergodicity. 15.2 V-Uniform Geometric Ergodicity. 15.3 Uniform Ergodicity. 15.4 Exercises. 15.5 Bibliographical Notes. 339 339 349 353 356 358 (ƒ, //Recurrence and Regularity. 361 16.1 (ƒ, /-/Recurrence and Drift Conditions. 361 16.2 (ƒ, //Regularity. 370 16.3 (ƒ, //Regularity of
the Skeletons. 377 16.4 (ƒ, //Regularity of the Split Kernel. 381 16.5 Exercises. 382 16.6 Bibliographical Notes. 383 Subgeometric Rates of Convergence. 17.1 (ƒ, //Ergodicity. 17.2 Drift Conditions. 17.3 Bibliographical Notes. 17.A Young Functions. 385 385 392 399 399 Uniform and V-Geometric Ergodicity by Operator Methods. 18.1 The Fixed-Point Theorem. 18.2 Dobrushin Coefficient and Uniform Ergodicity. 18.3 V-Dobrushin Coefficient. 18.4 V-Uniformly Geometrically Ergodic Markov Kernel. 18.5 Application of Uniform Ergodicity to the Existence of an Invariant Measure. 18.6 Exercises. 18.7 Bibliographical
Notes. 401 401 403 409 412 Coupling for Irreducible Kernels. 19.1 Coupling. 19.2 The Coupling Inequality. 19.3 Distributional, Exact, and Maximal Coupling. 19.4 A Coupling Proof of V-Geometric Ergodicity. 19.5 A Coupling Proof of Subgeometric Ergodicity. 421 422 432 435 441 444 Contents 19.6 19.7 Part IV 20 *vu Exercises. 449 Bibliographical Notes. 451 Selected Topics Convergence in the Wasserstein Distance. 20.1 The Wasserstein Distance. 20.2 Existence and Uniqueness of the Invariant Probability Measure. 20.3 Uniform Convergence in the Wasserstein Distance. 20.4 Nonuniform Geometric Convergence. 20.5 Subgeometric Rates of Convergence for the Wasserstein Distance. 20.6
Exercises. 20.7 Bibliographical Notes. 20.A Complements on the Wasserstein Distance. 455 456 21 Central Limit Theorems. 21.1 Preliminaries. 21.2 The Poisson Equation. 21.3 The Resolvent Equation. 21.4 A Martingale Coboundary Decomposition. 21.5 Exercises. 21.6 Bibliographical Notes. 21.A A Covariance Inequality. 489 490 495 503 508 517 519 520 22 Spectral Theory. 22.1 Spectrum. 22.2 Geometric and Exponential Convergence in L2(π). 22.3 Lp(u)-Exponential Convergence. 22.4 Cheeger’s Inequality . 22.5 Variance Bounds for Additive Functionals and the Central Limit Theorem for
Reversible Markov Chains. 22.6 Exercises. 22.7 Bibliographical Notes. 22.A Operators on Banach and Hilbert Spaces. 22.B Spectral Measure. 523 523 530 538 545 Concentration Inequalities . 23.1 Concentration Inequality for Independent Random Variables. 23.2 Concentration Inequality for Uniformly Ergodic Markov Chains. 23.3 Sub-Gaussian Concentration Inequalities for V-Geometrically Ergodic Markov Chains. 575 415 417 419 23 462 465 471 476 480 485 486 553 560 562 563 572 576 581 587
xviii Contents 23.4 Exponential Concentration Inequalities Under Wasserstein Contraction. Exercises. Bibliographical Notes. 594 599 601 Appendices. 603 A Notations. 605 В Topology, Measure and Probability. B.l Topology. B.2 Measures. B.3 Probability. 609 609 612 618 C Weak Convergence. C. 1 Convergence on Locally Compact Metric Spaces. C.2 Tightness. 625 625 626 D Total and V-Total Variation Distances. D.l Signed Measures. D.2 Total Variation
Distance. D.3 V-Total Variation. 629 629 631 635 E Martingales. E.l Generalized Positive Supermartingales. E.2 Martingales. E.3 Martingale Convergence Theorems. E.4 Central Limit Theorems. 637 637 638 639 641 F Mixing Coefficients. F.l Definitions. F.2 Properties. F.3 Mixing Coefficients of Markov Chains. 645 645 646 653 G Solutions to Selected Exercises. 657 References. 733 Index. 753 23.5 23.6 |
| any_adam_object | 1 |
| author | Douc, Randal 1971- Moulines, Eric 1963- Priouret, Pierre 1939- Soulier, Philippe |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV045443599 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-10T05:00:14Z |
| institution | BVB |
| isbn | 9783319977034 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030829087 |
| oclc_num | 1085676051 |
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| owner | DE-188 DE-91G DE-BY-TUM DE-83 DE-739 |
| owner_facet | DE-188 DE-91G DE-BY-TUM DE-83 DE-739 |
| physical | xviii, 757 Seiten Diagramme |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in operations research and financial engineering |
| spelling | Douc, Randal 1971- (DE-588)105018629X aut Markov Chains Randal Douc ; Eric Moulines ; Pierre Priouret ; Philippe Soulier Cham Springer [2018] xviii, 757 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Springer series in operations research and financial engineering Probability Theory and Stochastic Processes Distribution (Probability theory Markov-Kette (DE-588)4037612-6 gnd rswk-swf Markov-Kette (DE-588)4037612-6 s DE-604 Moulines, Eric 1963- (DE-588)1050741625 aut Priouret, Pierre 1939- (DE-588)173702538 aut Soulier, Philippe (DE-588)1178465055 aut Erscheint auch als Online-Ausgabe 978-3-319-97704-1 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030829087&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Douc, Randal 1971- Moulines, Eric 1963- Priouret, Pierre 1939- Soulier, Philippe Markov Chains Probability Theory and Stochastic Processes Distribution (Probability theory Markov-Kette (DE-588)4037612-6 gnd |
| subject_GND | (DE-588)4037612-6 |
| title | Markov Chains |
| title_auth | Markov Chains |
| title_exact_search | Markov Chains |
| title_full | Markov Chains Randal Douc ; Eric Moulines ; Pierre Priouret ; Philippe Soulier |
| title_fullStr | Markov Chains Randal Douc ; Eric Moulines ; Pierre Priouret ; Philippe Soulier |
| title_full_unstemmed | Markov Chains Randal Douc ; Eric Moulines ; Pierre Priouret ; Philippe Soulier |
| title_short | Markov Chains |
| title_sort | markov chains |
| topic | Probability Theory and Stochastic Processes Distribution (Probability theory Markov-Kette (DE-588)4037612-6 gnd |
| topic_facet | Probability Theory and Stochastic Processes Distribution (Probability theory Markov-Kette |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030829087&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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