Probability: theory and examples
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge, United Kingdom ; New York, NY, USA ; Port Melbourne, Australia ; New Delhi, India ; Singapore
Cambridge University Press
2019
|
| Ausgabe: | Fifth edition |
| Schriftenreihe: | Cambridge series in statistical and probabilistic mathematics
49 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030906716&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xii, 419 Seiten Illustrationen |
| ISBN: | 9781108473682 |
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| 245 | 1 | 0 | |a Probability |b theory and examples |c Rick Durrett (Duke University) |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0048 MAT 600f 2005 A 4008(5) 0104 MAT 600f 2005 A 4008(5) 0303 MAT 600f 2007 L 472(5) |
|---|---|
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| DE-BY-TUM_location | LSB 01 03 |
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| _version_ | 1821935470645346305 |
| adam_text | Contents Preface page xi Measure Theory 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Probability Spaces Distributions Random Variables Integration Properties of the Integral Expected Value 1.6.1 Inequalities 1.6.2 Integration to the Limit 1.6.3 Computing Expected Values Product Measures, Fubini’s Theorem Laws of Large Numbers 2.1 2.2 2.3 2.4 2.5 2.6 2.7 Independence 2.1.1 Sufficient Conditions for Independence 2.1.2 Independence, Distribution, and Expectation 2.1.3 Sums of Independent Random Variables 2.1.4 Constructing Independent Random Variables Weak Laws of Large Numbers 2.2.1 Ĺ1 Weak Laws 2.2.2 Triangular Arrays 2.2.3 Truncation Borel-Cantelli Lemmas Strong Law of Large Numbers Convergence of Random Series* 2.5.1 Rates of Convergence 2.5.2 Infinite Mean Renewal Theory* Large Deviations* Central Limit Theorems 3.1 3.2 The De Moivre-Laplace Theorem Weak Convergence VII 1 1 8 13 15 21 25 25 26 28 33 37 37 39 41 43 45 48 48 51 53 58 65 69 75 76 78 90 98 98 100
Contents viii 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.2.1 Exampies 3.2.2 Theory Characteristic Functions 3.3.1 Definition, Inversion Formula 3.3.2 Weak Convergence 3.3.3 Moments and Derivatives 3.3.4 Polya’s Criterion* 3.3.5 The Moment Problem* Central Limit Theorems 3.4.1 i.i.d. Sequences 3.4.2 Triangular Arrays 3.4.3 Prime Divisors (Erdös-Kac)* 3.4.4 Rates of Convergence (Berry-Esseen)* Local Limit Theorems* Poisson Convergence 3.6.1 The Basic Limit Theorem 3.6.2 Two Examples with Dependence Poisson Processes 3.7.1 Compound Poisson Processes 3.7.2 Thinning 3.7.3 Conditioning Stable Laws* Infinitely Divisible Distributions* Limit Theorems in 100 102 108 108 114 116 119 121 125 125 128 132 136 140 145 145 149 151 154 155 157 159 168 171 4 Martingales 4.1 Conditional Expectation 4.1.1 Examples 4.1.2 Properties 4.1.3 Regular Conditional Probabilities* 4.2 Martingales, Almost Sure Convergence 4.3 Examples 4.3.1 Bounded Increments 4.3.2 Polya’s Urn Scheme 4.3.3 Radon-Nikodym Derivatives 4.3.4 Branching Processes 4.4 Doob’s Inequality, Convergence inLp, p 1 4.5 Square Integrable Martingales* 4.6 Uniform Integrability, Convergence in L1 4.7 Backwards Martingales 4.8 Optional Stopping Theorems 4.8.1 Applications to Random Walks 4.9 Combinatorics of Simple Random Walk* 178 178 180 182 185 188 194 194 196 197 200 203 208 211 216 221 223 227 5 Markov Chains 5.1 Examples 5.2 Construction, Markov Properties 232 232 235
їх Contents 5.3 5.4 5.5 5.6 5.7 5.8 Recurrence and Transience Recurrence of Random Walks Stararred Section Stationary Measures Asymptotic Behavior Periodicity, Tail σ-Field* General State Space* 5.8.1 Recurrence and Transience 5.8.2 Stationary Measures 5.8.3 Convergence Theorem 5.8.4 GI/G/1 Queue Ergodic Theorems 6.1 6.2 6.3 6.4 6.5 Definitions and Examples Birkhoff’s Ergodic Theorem Recurrence A Subadditive Ergodic Theorem Applications Brownian Motion 7.1 7.2 7.3 7.4 7.5 7.6 Definition and Construction Markov Property, Blumenthaľs 0-1 Law Stopping Times, Strong Markov Property Path Properties 7.4.1 Zeros of Brownian Motion 7.4.2 Hitting Times Martingales Itô’s Formula* Applications to Random Walk 8.1 8.2 8.3 8.4 8.5 Donsker’s Theorem CLTs for Martingales CLTs for Stationary Sequences 8.3.1 Mixing Properties Empirical Distributions, Brownian Bridge Laws of the Iterated Logarithm Multidimensional Brownian Motion 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 Martingales Heat Equation Inhomogeneous Heat Equation Feynman-Kac Formula Dirichlet Problem 9.5.1 Exit Distributions Green’s Functions and Potential Kernels Poisson’s Equation 9.7.1 Occupation Times Schrôdinger Equation 243 248 259 268 274 278 281 281 282 283 286 286 289 293 296 300 305 305 311 316 320 320 321 325 328 336 336 342 347 351 354 360 364 364 366 368 370 373 377 379 382 385 387
Contents x Appendix A A.l A.2 A.3 A.4 A. 5 References Index Measure Theory Details Carathéodory’s Extension Theorem Which Sets Are Measurable? Kolmogorov’s Extension Theorem Radon-Nikodym Theorem Differentiating under the Integral 394 394 399 402 403 407 410 415
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| id | DE-604.BV045522439 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T18:29:18Z |
| institution | BVB |
| isbn | 9781108473682 |
| language | English |
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| spellingShingle | Durrett, Richard 1951- Probability theory and examples Cambridge series in statistical and probabilistic mathematics Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4064324-4 (DE-588)4143389-0 |
| title | Probability theory and examples |
| title_auth | Probability theory and examples |
| title_exact_search | Probability theory and examples |
| title_full | Probability theory and examples Rick Durrett (Duke University) |
| title_fullStr | Probability theory and examples Rick Durrett (Duke University) |
| title_full_unstemmed | Probability theory and examples Rick Durrett (Duke University) |
| title_short | Probability |
| title_sort | probability theory and examples |
| title_sub | theory and examples |
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| topic_facet | Wahrscheinlichkeitstheorie Wahrscheinlichkeitsrechnung Aufgabensammlung |
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Inhaltsverzeichnis
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| Signatur: |
0048 MAT 600f 2005 A 4008(5)
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|---|---|
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0104 MAT 600f 2005 A 4008(5)
Lageplan |
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| Exemplar 1 | Ausleihbar Am Standort |
Teilbibliothek Chemie, Lehrbuchsammlung
| Signatur: |
0303 MAT 600f 2007 L 472(5)
Lageplan |
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| Exemplar 1 | Ausleihbar Am Standort |
| Exemplar 2 | Ausleihbar Am Standort |
| Exemplar 3 | Ausleihbar Unterwegs |
| Exemplar 4 | Ausleihbar Ausgeliehen – Rückgabe bis: 14.04.2025 |
| Exemplar 5 | Ausleihbar Am Standort |