Applied stochastic analysis
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| Hauptverfasser: | , , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2019]
|
| Schriftenreihe: | Graduate studies in mathematics
199 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 245 | 1 | 0 | |a Applied stochastic analysis |c Weinan E, Tiejun Li, Eric Vanden-Eijnden |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2019] | |
| 264 | 4 | |c © 2019 | |
| 300 | |a xxi, 305 Seiten | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics |v 199 | |
| 650 | 0 | 7 | |a Stochastische Analysis |0 (DE-588)4132272-1 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0202/MAT 606f 2019 B 1092 |
|---|---|
| DE-BY-TUM_katkey | 2400099 |
| DE-BY-TUM_media_number | 040008859614 |
| _version_ | 1816714508802981888 |
| adam_text | Contents Introduction to the Series xiii Preface xvii Notation xix Part 1. Fundamentals Random Variables З §1.1. Elementary Examples З §1.2. Probability Space 5 §1.3. Conditional Probability 6 §1.4. Discrete Distributions 7 §1.5. Continuous Distributions 8 §1.6. Independence 12 §1.7. Conditional Expectation 14 §1.8. Notions of Convergence 16 §1.9. Characteristic Function 17 Chapter 1. §1.10. Generating Function and Cumulants 19 §1.11. The Borel-Cantelli Lemma 21 Exercises 24 Notes 27 Chapter 2. Limit Theorems 29 §2.1. The Law of Large Numbers 29 §2.2. Central Limit Theorem 31
§2.3. Cramer’s Theorem for Large Deviations 32 §2.4. Statistics of Extrema Exercises 40 42 Notes 44 Chapter 3. Markov Chains 45 46 §3.1. §3.2. Discrete Time Finite Markov Chains Invariant Distribution §3.3. §3.4. §3.5. Ergodic Theorem for Finite Markov Chains Poisson Processes Q-prcæesses 51 §3.6. §3.7. Embedded Chain and Irreducibility Ergodic Theorem for Q-processes 57 §3.8. §3.9. Time Reversal Hidden Markov Model 59 61 48 53 54 59 §3.10. Networks and Markov Chains Exercises 67 Notes 73 Chapter 4. Monte Carlo Methods §4.1. Numerical Integration §4.2. Generation of Random Variables §4.3. §4.4. Variance Reduction The Metropolis Algorithm §4.5. Kinetic Monte Carlo §4.6. Simulated Tempering 71 75 76 77 83 87 91 92 94 §4.7. Simulated Annealing Exercises 96 Notes 98 Chapter 5. Stochastic Processes 101 §5.1. §5.2. Axiomatic Construction of Stochastic Process Filtration and Stopping Time 102 §5.3. Markov Processes 106 109 §5.4. Gaussian Processes Exercises Notes 104 113 114
Chapter 6. Wiener Process 117 118 §6.1. The Diffusion Limit of Random Walks §6.2. §6.3. The Invariance Principle Wiener Process as a Gaussian Process 120 §6.4. Wiener Process as a Markov Process 125 §6.5. Properties of the Wiener Process 126 §6.6. §6.7. Wiener Process under Constraints Wiener Chaos Expansion 130 Exercises Notes Chapter 7. Stochastic Differential Equations 121 132 135 137 139 §7.1. §7.2. ltd Integral Itô’s Formula 140 144 §7.3. §7.4. Stochastic Differential Equations Stratonovich Integral 148 154 §7.5. Numerical Schemes and Analysis 156 §7.6. Multilevel Monte Carlo Method 162 Exercises 165 167 Notes Chapter 8. Fokker-Planck Equation 169 170 §8.1. Fokker-Planck Equation §8.2. Boundary Condition §8.3. §8.4. The Backward Equation Invariant Distribution §8.5. §8.6. The Markov Semigroup Feynman-Kac Formula 178 180 §8.7. §8.8. Boundary Value Problems Spectral Theory 181 183 173 175 176 §8.9. Asymptotic Analysis of SDEs §8.10. Weak Convergence 185 188 Exercises 193 194 Notes
Part 2. Advanced Topics Chapter 9. Path Integral §9.1. Formal Wiener Measure §9.2. Girsanov Transformation §9.3. Feynman-Kac Formula Revisited Exercises Notes Chapter 10. §10.1. Random Fields Examples of Random Fields 199 200 203 207 208 208 209 210 §10.2. Gaussian Random Fields §10.3. Gibbs Distribution and Markov Random Fields Exercise 214 Notes 216 Chapter 11. Introduction to Statistical Mechanics 212 216 217 §11.1. §11.2. Thermodynamic Heuristics Equilibrium Statistical Mechanics 219 224 §11.3. §11.4. §11.5. Generalized Langevin Equation Linear Response Theory The Mori-Zwanzig Reduction 233 §11.6. Kac-Zwanzig Model Exercises Notes Chapter 12. 240 242 244 Rare Events §12.1. Metastability and Transition Events §12.2. §12.3. WKB Analysis Transition Rates §12.4. §12.5. Large Deviation Theory and Transition Paths Computing the Minimum Energy Paths §12.6. Quasipotential and Energy Landscape Exercises Notes 236 238 245 246 248 249 250 253 254 259 260
Chapter 13. Introduction to Chemical Reaction Kinetics 261 262 §13.1. §13.2. Reaction Rate Equations Chemical Master Equation §13.3. Stochastic Differential Equations 263 265 §13.4. Stochastic Simulation Algorithm 266 §13.5. §13.6. The Large Volume Limit Diffusion Approximation 266 268 §13.7. §13.8. The Tau-leaping Algorithm Stationary Distribution 269 §13.9. Muffiscale Analysis of a Chemical Kinetic System 271 272 Exercises 277 Notes 277 Appendix 279 A. Laplace Asymptotics and Varadhan’s Lemma B. Gronwalľs Inequality 279 281 C. Measure and Integration D. Martingales E. Strong Markov Property 282 284 F. Semigroup of Operators 286 285 Bibliography 289 Index 301
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| any_adam_object | 1 |
| author | E, Weinan 1963- Li, Tiejun 1974- Vanden-Eijnden, Eric 1968- |
| author_GND | (DE-588)139594116 (DE-588)118986102X (DE-588)1182918263 |
| author_facet | E, Weinan 1963- Li, Tiejun 1974- Vanden-Eijnden, Eric 1968- |
| author_role | aut aut aut |
| author_sort | E, Weinan 1963- |
| author_variant | w e we t l tl e v e eve |
| building | Verbundindex |
| bvnumber | BV045538701 |
| classification_rvk | SK 820 |
| classification_tum | MAT 606f |
| ctrlnum | (OCoLC)1107327586 (DE-599)BVBBV045538701 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV045538701 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-25T17:57:35Z |
| institution | BVB |
| isbn | 9781470465698 9781470449339 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030922680 |
| oclc_num | 1107327586 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-188 DE-83 DE-739 DE-703 |
| owner_facet | DE-91G DE-BY-TUM DE-188 DE-83 DE-739 DE-703 |
| physical | xxi, 305 Seiten |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spellingShingle | E, Weinan 1963- Li, Tiejun 1974- Vanden-Eijnden, Eric 1968- Applied stochastic analysis Graduate studies in mathematics Stochastische Analysis (DE-588)4132272-1 gnd |
| subject_GND | (DE-588)4132272-1 |
| title | Applied stochastic analysis |
| title_auth | Applied stochastic analysis |
| title_exact_search | Applied stochastic analysis |
| title_full | Applied stochastic analysis Weinan E, Tiejun Li, Eric Vanden-Eijnden |
| title_fullStr | Applied stochastic analysis Weinan E, Tiejun Li, Eric Vanden-Eijnden |
| title_full_unstemmed | Applied stochastic analysis Weinan E, Tiejun Li, Eric Vanden-Eijnden |
| title_short | Applied stochastic analysis |
| title_sort | applied stochastic analysis |
| topic | Stochastische Analysis (DE-588)4132272-1 gnd |
| topic_facet | Stochastische Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030922680&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009739289 |
| work_keys_str_mv | AT eweinan appliedstochasticanalysis AT litiejun appliedstochasticanalysis AT vandeneijndeneric appliedstochasticanalysis |