Ergodic behavior of Markov processes: with applications to limit theorems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2018]
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| Schriftenreihe: | De Gruyter Studies in Mathematics
volume 67 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 256 Seiten |
| ISBN: | 9783110458701 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804177747900104704 |
|---|---|
| adam_text | Contents Introduction—1 Part I: 1 1.1 1.2 1.2.1 1.2.2 1.2.3 1.2.4 1.3 1.4 Ergodic Rates for Markov Chains and Processes Markov Chains with Discrete State Spaces — 7 Basic Definitions and Facts — 7 Ergodic Theorem — 9 Ergodic Theorem for Finite MCs — 9 “Analytic” Proof of Theorem 1.2.1: Contraction Argument —11 “Probabilistic” Proof of Theorem 1.2.1: Coupling Argument—13 Recurrence and Transience. Ergodic Theorem for Countable MCs —15 Stationary MCs: Ergodicity, Mixing, and Limit Theorems —17 Comments — 23 2.9 2.10 General Markov Chains: Ergodicity In Total Variation — 25 Basic Definitions and Facts — 25 Total Variation Distance and the Coupling Lemma — 27 Uniform Ergodicity: The Dobrushin theorem — 33 Preliminaries to Nonuniform Ergodicity: Motivation and Auxiliaries — 36 Stabilization of Transition Probabilities: Doob’s Theorem----- 40 Nonuniform Ergodicity at Exponential Rate: The Harris Theorem — 45 Nonuniform Ergodicity at Subexponential Rates — 50 Lyapunov-Type Conditions — 55 Linear Lyapunov-Type Condition and Exponential Ergodicity — 55 Lyapunov-Type Condition for Cesàro Means of Moments — 58 Sublinear Lyapunov-Type Conditions and Subexponential Ergodicity — 59 Dobrushin Condition: Sufficient Conditions and Alternatives — 67 Comments------ 71 3 3.1 3.2 3.3 3.3.1 3.3.2 3.3.3 3.4 3.4.1 3.4.2 3.4.3 Markov Processes with Continuous Time — 73 Basic Definitions and Facts — 73 Ergodicity in Total Variation: The Skeleton Chain Approach — 74 Diffusion Processes------ 85 Lyapunov-Type Conditions — 85 Dobrushin Condition — 90 Summary—91 Solutions to Lévy-Driven SDEs-------- 93
Lyapunov-Type Condition: “Light Tails” Case — 94 Lyapunov-Type Condition: “Heavy Tails” Case —103 Dobrushin Condition------ 107 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.8.1 2.8.2 2.8.3
X — Contents Summary —109 Comments —112 3.4.4 3.5 4 Weak Ergodic Rates —114 4.1 Markov Models with Intrinsic Memory—114 4.2 Dissipative Stochastic Systems —117 4.2.1 Warm-up” Calculation: Diffusions —117 4.2.2 Dissipatlvity for a Solution to SDDE —119 4.3 Coupling Distances for Probability Measures —122 4.4 Measurable Selections and General Coupling Lemma for Probability Kernels —128 4.5 Weak Ergodic Rates —133 4.6 Application to Stochastic Delay Equations—140 4.6.1 Lyapunov-Type Conditions —141 4.6.2 Generalized Couplings and Construction of d(x,y)—143 4.6.3 Summary—153 4.7 Comments —155 Partii: Limit Theorems 5 5.1 5.2 5.2.1 5.2.2 5.3 5.3.1 5.3.2 5.4 The Law of Large Numbers and the Central Limit Theorem —159 Preliminaries —159 The CLT for Weakly Ergodic Markov Chains—166 The Martingale CLT—166 The CLT for a Weakly Ergodic Markov Chain —170 Extensions —175 Non-Stationary Setting—175 Continuous-Time Setting —178 Comments —181 6 6.1 6.2 6.3 6.3.1 6.3.2 Functional Limit Theorems —183 Preliminaries —183 Autoregressive Models with Markov Regime —186 The Time Delay Method for General Autoregressive Models — 205 General Statements — 206 Averaging Principle and Diffusion Approximation for Systems with Fast Markov Perturbations — 216 A Fully Coupled System with Dissipative Fast Component—230 Comments — 246 6.3.3 6.4 Bibliography— 249 Index—255
|
| any_adam_object | 1 |
| author | Kulik, Alexei 1972- |
| author_GND | (DE-588)1120029015 |
| author_facet | Kulik, Alexei 1972- |
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| building | Verbundindex |
| bvnumber | BV044439383 |
| classification_rvk | SK 820 |
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| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| publisher | De Gruyter |
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| series | De Gruyter Studies in Mathematics |
| series2 | De Gruyter Studies in Mathematics |
| spelling | Kulik, Alexei 1972- Verfasser (DE-588)1120029015 aut Ergodic behavior of Markov processes with applications to limit theorems Alexei Kulik Berlin ; Boston De Gruyter [2018] © 2018 X, 256 Seiten txt rdacontent n rdamedia nc rdacarrier De Gruyter Studies in Mathematics volume 67 Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Markov processes ergodic rates ergodicity limit theorems Markov-Prozess (DE-588)4134948-9 s Ergodentheorie (DE-588)4015246-7 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-045893-0 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-045871-8 De Gruyter Studies in Mathematics volume 67 (DE-604)BV000005407 67 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=029840587&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kulik, Alexei 1972- Ergodic behavior of Markov processes with applications to limit theorems De Gruyter Studies in Mathematics Ergodentheorie (DE-588)4015246-7 gnd Markov-Prozess (DE-588)4134948-9 gnd |
| subject_GND | (DE-588)4015246-7 (DE-588)4134948-9 |
| title | Ergodic behavior of Markov processes with applications to limit theorems |
| title_auth | Ergodic behavior of Markov processes with applications to limit theorems |
| title_exact_search | Ergodic behavior of Markov processes with applications to limit theorems |
| title_full | Ergodic behavior of Markov processes with applications to limit theorems Alexei Kulik |
| title_fullStr | Ergodic behavior of Markov processes with applications to limit theorems Alexei Kulik |
| title_full_unstemmed | Ergodic behavior of Markov processes with applications to limit theorems Alexei Kulik |
| title_short | Ergodic behavior of Markov processes |
| title_sort | ergodic behavior of markov processes with applications to limit theorems |
| title_sub | with applications to limit theorems |
| topic | Ergodentheorie (DE-588)4015246-7 gnd Markov-Prozess (DE-588)4134948-9 gnd |
| topic_facet | Ergodentheorie Markov-Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029840587&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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