Knowing the odds: an introduction to probability
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2012
|
| Schriftenreihe: | Graduate studies in mathematics
139 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 413 - 414 |
| Beschreibung: | XVI, 421 S. graph. Darst. |
| ISBN: | 9780821885321 |
Internformat
MARC
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| 245 | 1 | 0 | |a Knowing the odds |b an introduction to probability |c John B. Walsh |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2012 | |
| 300 | |a XVI, 421 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Graduate studies in mathematics |v 139 | |
| 500 | |a Literaturverz. S. 413 - 414 | ||
| 650 | 4 | |a Probabilities | |
| 650 | 7 | |a Probability theory and stochastic processes -- Instructional exposition (textbooks, tutorial papers, etc.) |2 msc | |
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Datensatz im Suchindex
| _version_ | 1804149427521191936 |
|---|---|
| adam_text | Titel: Knowing the odds
Autor: Walsh, John B
Jahr: 2012
Contents
Preface xi
Introduction xiii
Chapter 1. Probability Spaces 1
§1.1. Sets and Sigma-Fields 1
§1.2. Elementary Properties of Probability Spaces 6
§1.3. The Intuition 8
§1.4. Conditional Probability 15
§1.5. Independence 18
§1.6. Counting: Permutations and Combinations 22
§1.7. The Gambler s Ruin 30
Chapter 2. Random Variables 39
§2.1. Random Variables and Distributions 39
§2.2. Existence of Random Variables 45
§2.3. Independence of Random Variables 48
§2.4. Types of Distributions 49
§2.5. Expectations I: Discrete Random Variables 54
§2.6. Moments, Means and Variances 60
§2.7. Mean, Median, and Mode 63
§2.8. Special Discrete Distributions 65
Chapter 3. Expectations II: The General Case 75
§3.1. From Discrete to Continuous 75
viii Contents
§3.2. The Expectation as an Integral 81
§3.3. Some Moment Inequalities 85
§3.4. Convex Functions and Jensen s Inequality 86
§3.5. Special Continuous Distributions 89
§3.6. Joint Distributions and Joint Densities 96
§3.7. Conditional Distributions, Densities, and Expectations 103
Chapter 4. Convergence 117
§4.1. Convergence of Random Variables 117
§4.2. Convergence Theorems for Expectations 122
§4.3. Applications 127
Chapter 5. Laws of Large Numbers 133
§5.1. The Weak and Strong Laws 134
§5.2. Normal Numbers 137
§5.3. Sequences of Random Variables: Existence* 140
§5.4. Sigma Fields as Information 142
§5.5. Another Look at Independence 144
§5.6. Zero-one Laws 145
Chapter 6. Convergence in Distribution and the CLT 151
§6.1. Characteristic Functions 151
§6.2. Convergence in Distribution 162
§6.3. Levy s Continuity Theorem 170
§6.4. The Central Limit Theorem 176
§6.5. Stable Laws* 182
Chapter 7. Markov Chains and Random Walks 191
§7.1. Stochastic Processes 191
§7.2. Markov Chains 192
§7.3. Classification of States 201
§7.4. Stopping Times 204
§7.5. The Strong Markov Property 208
§7.6. Recurrence and Transience 211
§7.7. Equilibrium and the Ergodic Theorem for Markov Chains 218
§7.8. Finite State Markov Chains 226
§7.9. Branching Processes 234
§7.10. The Poisson Process 242
Contents ix
§7.11. Birth and Death Processes* 250
Chapter 8. Conditional Expectations 265
§8.1. Conditional Expectations 265
§8.2. Elementary Properties 268
§8.3. Approximations and Projections 272
Chapter 9. Discrete-Parameter Martingales 275
§9.1. Martingales 275
§9.2. System Theorems 282
§9.3. Convergence 290
§9.4. Uniform Integrability 295
§9.5. Applications 304
§9.6. Financial Mathematics I: The Martingale Connection* 315
Chapter 10. Brownian Motion 335
§10.1. Standard Brownian Motion 336
§10.2. Stopping Times and the Strong Markov Property 344
§10.3. The Zero Set of Brownian Motion 348
§10.4. The Reflection Principle 351
§10.5. Recurrence and Hitting Properties 352
§10.6. Path Irregularity 354
§10.7. The Brownian Infinitesimal Generator* 359
§10.8. Related Processes 363
§10.9. Higher Dimensional Brownian Motion 368
§10.10. Financial Mathematics II: The Black-Scholes Model* 374
§10.11. Skorokhod Embedding* 377
§10.12. Levy s Construction of Brownian Motion* 388
§10.13. The Ornstein-Uhlenbeck Process* 390
§10.14. White Noise and the Wiener Integral* 394
§10.15. Physical Brownian Motion* 404
§10.16. What Brownian Motion Really Does 410
Bibliography 413
Index 415
|
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| isbn | 9780821885321 |
| language | English |
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| spelling | Walsh, John B. Verfasser (DE-588)139897658 aut Knowing the odds an introduction to probability John B. Walsh Providence, RI American Mathematical Society 2012 XVI, 421 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 139 Literaturverz. S. 413 - 414 Probabilities Probability theory and stochastic processes -- Instructional exposition (textbooks, tutorial papers, etc.) msc Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 Stochastischer Prozess (DE-588)4057630-9 s Graduate studies in mathematics 139 (DE-604)BV009739289 139 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025237725&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Walsh, John B. Knowing the odds an introduction to probability Graduate studies in mathematics Probabilities Probability theory and stochastic processes -- Instructional exposition (textbooks, tutorial papers, etc.) msc Stochastischer Prozess (DE-588)4057630-9 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4079013-7 |
| title | Knowing the odds an introduction to probability |
| title_auth | Knowing the odds an introduction to probability |
| title_exact_search | Knowing the odds an introduction to probability |
| title_full | Knowing the odds an introduction to probability John B. Walsh |
| title_fullStr | Knowing the odds an introduction to probability John B. Walsh |
| title_full_unstemmed | Knowing the odds an introduction to probability John B. Walsh |
| title_short | Knowing the odds |
| title_sort | knowing the odds an introduction to probability |
| title_sub | an introduction to probability |
| topic | Probabilities Probability theory and stochastic processes -- Instructional exposition (textbooks, tutorial papers, etc.) msc Stochastischer Prozess (DE-588)4057630-9 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Probabilities Probability theory and stochastic processes -- Instructional exposition (textbooks, tutorial papers, etc.) Stochastischer Prozess Wahrscheinlichkeitstheorie |
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