Probability via expectation:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Springer
1992
|
| Edition: | 3. ed. |
| Series: | Springer texts in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Frühere Ausg. u.d.T.: Whittle, Peter: Probability |
| Physical Description: | XVIII, 300 S. graph. Darst. |
| ISBN: | 0387977643 3540977643 0387977589 3540977589 |
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MARC
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| 100 | 1 | |a Whittle, Peter |d 1927-2021 |e Verfasser |0 (DE-588)119218267 |4 aut | |
| 245 | 1 | 0 | |a Probability via expectation |c Peter Whittle |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a New York u.a. |b Springer |c 1992 | |
| 300 | |a XVIII, 300 S. |b graph. Darst. | ||
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| 490 | 0 | |a Springer texts in statistics | |
| 500 | |a Frühere Ausg. u.d.T.: Whittle, Peter: Probability | ||
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Record in the Search Index
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Contents
Preface to the Third Edition vii
Preface to Probability (1970) xi
Preface to the Russian Edition of Probability (1982) xiii
CHAPTER 1
Uncertainty, Intuition and Expectation 1
1. Ideas and Examples 1
2. The Empirical Basis 2
3. Averages over a Finite Population 5
4. Repeated Sampling: Expectation 8
5. More on Sample Spaces and Variables 10
6. Ideal and Actual Experiments: Observables 11
CHAPTER 2
Expectation 13
1. Random Variables 13
2. Axioms for the Expectation Operator 14
3. Events: Probability 16
4. Some Examples of an Expectation 17
5. Moments 21
6. Applications: Optimization Problems 22
7. Equiprobable Outcomes: Sample Surveys 24
8. Applications: Least Square Estimation of Random Variables 28
9. Some Implications of the Axioms 32
CHAPTER 3
Probability 38
1. Events, Sets and Indicators 38
2. Probability Measure 42
xv
xvi Contents
3. Expectation as a Probability Integral 44
4. Some History 45
5. Subjective Probability 47
CHAPTER 4
Some Basic Models 49
1. A Model of Spatial Distribution 49
2. The Multinomial, Binomial, Poisson and Geometric Distributions 52
3. Independence 56
4. Probability Generating Functions 59
5. The St. Petersburg Paradox 63
6. Matching, and Other Combinatorial Problems 66
7. Conditioning 68
8. Variables on the Continuum: the Exponential and
Gamma Distributions 73
CHAPTER 5
Conditioning 77
1. Conditional Expectation 77
2. Conditional Probability 81
3. A Conditional Expectation as a Random Variable 85
4. Conditioning on a c Field 89
5. Independence 89
6. Statistical Decision Theory 92
7. Information Transmission 94
8. Acceptance Sampling 97
CHAPTER 6
Applications of the Independence Concept 100
1. Renewal Processes 100
2. Recurrent Events: Regeneration Points 105
3. A Result in Statistical Mechanics: the Gibbs Distribution 109
4. Branching Processes 113
CHAPTER 7
The Two Basic Limit Theorems 119
1. Convergence in Distribution (Weak Convergence) 119
2. Properties of the Characteristic Function 122
3. The Law of Large Numbers 126
4. Normal Convergence (the Central Limit Theorem) 127
5. The Normal Distribution 129
CHAPTER 8
Continuous Random Variables and Their Transformations 136
1. Distributions with a Density 136
2. Functions of Random Variables 139
3. Conditional Densities 142
Contents xvii
CHAPTER 9
Markov Processes in Discrete Time 145
1. Stochastic Processes and the Markov Property 145
2. The Case of a Discrete State Space: the Kolmogorov Equations 151
3. Some Examples: Ruin, Survival and Runs 156
4. Birth and Death Processes: Detailed Balance 159
5. Some Examples We Should Like to Defer 161
6. Random Walks, Random Stopping and Ruin 162
7. Auguries of Martingales 168
8. Recurrence and Equilibrium 169
9. Recurrence and Dimension 173
CHAPTER 10
Markov Processes in Continuous Time 175
1. The Markov Property in Continuous Time 175
2. The Case of a Discrete State Space 176
3. The Poisson Process 179
4. Birth and Death Processes 180
5. Processes on Nondiscrete State Spaces 183
6. The Filing Problem 186
7. Some Continuous Time Martingales 187
8. Stationarity and Reversibility 189
9. The Ehrenfest Model 192
10. Processes of Independent Increments 194
11. Brownian Motion: Diffusion Processes 198
12. First Passage and Recurrence for Brownian Motion 202
CHAPTER 11
Second Order Theory 206
1. Back to L2 206
2. Linear Least Square Approximation 208
3. Projection: Innovation 210
4. The Gauss Markov Theorem 213
5. The Convergence of Linear Least Square Estimates 215
6. Direct and Mutual Mean Square Convergence 217
7. Conditional Expectations as Least Square Estimates:
Martingale Convergence 218
CHAPTER 12
Consistency and Extension: the Finite Dimensional Case 221
1. The Issues 221
2. Convex Sets 222
3. The Consistency Condition for Expectation Values 227
4. The Extension of Expectation Values 228
5. Examples of Extension 230
6. Dependence Information: Chernoff Bounds 233
xviii Contents
CHAPTER 13
Stochastic Convergence 235
1. The Characterization of Convergence 235
2. Types of Convergence 237
3. Some Consequences 239
4. Convergence in rth Mean 240
CHAPTER 14
Martingales 243
1. The Martingale Property 243
2. Kolmogorov's Inequality: the Law of Large Numbers 247
3. Martingale Convergence: Applications 250
4. The Optional Stopping Theorem 253
5. Examples of Stopped Martingales 255
CHAPTER 15
Extension: Examples of the Infinite Dimensional Case 258
1. Generalities on the Infinite Dimensional Case 258
2. Fields and ff Fields of Events 259
3. Extension on a Linear Lattice 260
4. Integrable Functions of a Scalar Random Variable 263
5. Expectations Derivable from the Characteristic Function:
Weak Convergence 265
CHAPTER 16
Some Interesting Processes 270
1. Information Theory: Block Coding 270
2. Information Theory: More on the Shannon Measure 273
3. Information Theory: Sequential Interrogation and Questionnaires 275
4. Dynamic Optimization 277
5. Quantum Mechanics: the Static Case 283
6. Quantum Mechanics: the Dynamic Case 289
References 293
Index 295 |
| any_adam_object | 1 |
| author | Whittle, Peter 1927-2021 |
| author_GND | (DE-588)119218267 |
| author_facet | Whittle, Peter 1927-2021 |
| author_role | aut |
| author_sort | Whittle, Peter 1927-2021 |
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| building | Verbundindex |
| bvnumber | BV005527168 |
| callnumber-first | Q - Science |
| callnumber-label | QA273 |
| callnumber-raw | QA273.W59 1992 |
| callnumber-search | QA273.W59 1992 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 170 SK 800 |
| classification_tum | MAT 600f |
| ctrlnum | (OCoLC)263574256 (DE-599)BVBBV005527168 |
| dewey-full | 519.220 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 20 |
| dewey-search | 519.2 20 |
| dewey-sort | 3519.2 220 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV005527168 |
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| indexdate | 2025-02-10T09:01:22Z |
| institution | BVB |
| isbn | 0387977643 3540977643 0387977589 3540977589 |
| language | English |
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| physical | XVIII, 300 S. graph. Darst. |
| publishDate | 1992 |
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| spelling | Whittle, Peter 1927-2021 Verfasser (DE-588)119218267 aut Probability via expectation Peter Whittle 3. ed. New York u.a. Springer 1992 XVIII, 300 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer texts in statistics Frühere Ausg. u.d.T.: Whittle, Peter: Probability Probabilities Wahrscheinlichkeit (DE-588)4137007-7 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Wahrscheinlichkeit (DE-588)4137007-7 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003463643&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Whittle, Peter 1927-2021 Probability via expectation Probabilities Wahrscheinlichkeit (DE-588)4137007-7 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4137007-7 (DE-588)4079013-7 (DE-588)4064324-4 (DE-588)4151278-9 |
| title | Probability via expectation |
| title_auth | Probability via expectation |
| title_exact_search | Probability via expectation |
| title_full | Probability via expectation Peter Whittle |
| title_fullStr | Probability via expectation Peter Whittle |
| title_full_unstemmed | Probability via expectation Peter Whittle |
| title_short | Probability via expectation |
| title_sort | probability via expectation |
| topic | Probabilities Wahrscheinlichkeit (DE-588)4137007-7 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Probabilities Wahrscheinlichkeit Wahrscheinlichkeitstheorie Wahrscheinlichkeitsrechnung Einführung |
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