Probability via expectation:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York ; Berlin ; Heidelberg ; Barcelona ; Hong Kong ; London
Springer
2000
|
| Edition: | 4. ed. |
| Series: | Springer texts in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 341 - 344 |
| Physical Description: | XXI, 352 S. graph. Darst. : 24 cm |
| ISBN: | 0387989552 |
Staff View
MARC
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| 245 | 1 | 0 | |a Probability via expectation |c Peter Whittle |
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Record in the Search Index
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| adam_text | Contents
Preface to the Fourth Edition vii
Preface to the Third Edition ix
Preface to the Russian Edition of Probability (1982) xiii
Preface to Probability (1970) xv
1 Uncertainty, Intuition, and Expectation 1
1 Ideas and Examples 1
2 The Empirical Basis 3
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
2 Expectation 13
1 Random Variables 13
2 Axioms for the Expectation Operator 14
3 Events: Probability 17
4 Some Examples of an Expectation 18
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
xviii Contents
3 Probability 39
1 Events, Sets and Indicators 39
2 Probability Measure 43
3 Expectation as a Probability Integral 46
4 Some History 47
5 Subjective Probability 49
4 Some Basic Models 51
1 A Model of Spatial Distribution 51
2 The Multinomial, Binomial, Poisson and Geometric
Distributions 54
3 Independence 58
4 Probability Generating Functions 61
5 The St. Petersburg Paradox 66
6 Matching, and Other Combinatorial Problems 68
7 Conditioning 71
8 Variables on the Continuum: The Exponential and
Gamma Distributions 76
5 Conditioning 80
1 Conditional Expectation 80
2 Conditional Probability 84
3 A Conditional Expectation as a Random Variable 88
4 Conditioning on a a Field 92
5 Independence 93
6 Statistical Decision Theory 95
7 Information Transmission 97
8 Acceptance Sampling 99
6 Applications of the Independence Concept 102
1 Renewal Processes 102
2 Recurrent Events: Regeneration Points 107
3 A Result in Statistical Mechanics: The Gibbs
Distribution Ill
4 Branching Processes 115
7 The Two Basic Limit Theorems 121
1 Convergence in Distribution (Weak Convergence) 121
2 Properties of the Characteristic Function 124
3 The Law of Large Numbers 129
4 Normal Convergence (the Central Limit Theorem) 130
5 The Normal Distribution 132
6 The Law of Large Numbers and the Evaluation
of Channel Capacity 138
Contents xix
8 Continuous Random Variables and Their Transformations 141
1 Distributions with a Density 141
2 Functions of Random Variables 144
3 Conditional Densities 148
9 Markov Processes in Discrete Time 150
1 Stochastic Processes and the Markov Property 150
2 The Case of a Discrete State Space: The Kolmogorov
Equations 156
3 Some Examples: Ruin, Survival and Runs 162
4 Birth and Death Processes: Detailed Balance 165
5 Some Examples We Should Like to Defer 167
6 Random Walks, Random Stopping and Ruin 168
7 Auguries of Martingales 174
8 Recurrence and Equilibrium 175
9 Recurrence and Dimension 179
10 Markov Processes in Continuous Time 182
1 The Markov Property in Continuous Time 182
2 The Case of a Discrete State Space 183
3 The Poisson Process 186
4 Birth and Death Processes 187
5 Processes on Nondiscrete State Spaces 192
6 The Filing Problem 195
7 Some Continuous Time Martingales 196
8 Stationarity and Reversibility 197
9 The Ehrenfest Model 200
10 Processes of Independent Increments 203
11 Brownian Motion: Diffusion Processes 207
12 First Passage and Recurrence for Brownian Motion 211
11 Action Optimisation; Dynamic Programming 215
1 Action Optimisation 215
2 Optimisation over Time: the Dynamic Programming Equation . . 216
3 State Structure 217
4 Optimal Control Under LQG Assumptions 220
5 Minimal Length Coding 221
6 Discounting 223
7 Continuous Time Versions and Infinite Horizon Limits 225
8 Policy Improvement 227
12 Optimal Resource Allocation 229
1 Portfolio Selection in Discrete Time 229
2 Portfolio Selection in Continuous Time 232
xx Contents
3 Multi Armed Bandits and the Gittins Index 232
4 Open Processes 236
5 Tax Problems 238
13 Finance: Risk Free Trading and Option Pricing 241
1 Options and Hedging Strategies 241
2 Optimal Targeting of the Contract 243
3 An Example 245
4 A Continuous Time Model 246
5 How Should it Be Done? 248
14 Second Order Theory 253
1 Back to L2 253
2 Linear Least Square Approximation 256
3 Projection: Innovation 257
4 The Gauss Markov Theorem 260
5 The Convergence of Linear Least Square Estimates 262
6 Direct and Mutual Mean Square Convergence 264
7 Conditional Expectations as Least Square Estimates:
Martingale Convergence 266
15 Consistency and Extension: The Finite Dimensional Case 268
1 The Issues 268
2 Convex Sets 269
3 The Consistency Condition for Expectation Values 274
4 The Extension of Expectation Values 275
5 Examples of Extension 277
6 Dependence Information: Chernoff Bounds 280
16 Stochastic Convergence 282
1 The Characterization of Convergence 282
2 Types of Convergence 284
3 Some Consequences 286
4 Convergence in rth Mean 287
17 Martingales 290
1 The Martingale Property 290
2 Kolmogorov s Inequality: the Law of Large Numbers 294
3 Martingale Convergence: Applications 298
4 The Optional Stopping Theorem 301
5 Examples of Stopped Martingales . . . . , 303
18 Large Deviation Theory 306
1 The Large Deviation Property 306
2 Some Preliminaries 307
3 Cramer s Theorem 309
Contents xxi
4 Some Special Cases 310
5 Circuit Switched Networks and Boltzmann Statistics 311
6 Multi Class Traffic and Effective Bandwidth 313
7 Birth and Death Processes 314
19 Extension: Examples of the Infinite Dimensional Case 317
1 Generalities on the Infinite Dimensional Case 317
2 Fields and a Fields of Events 318
3 Extension on a Linear Lattice 319
4 Integrable Functions of a Scalar Random Variable 322
5 Expectations Derivable from the Characteristic Function:
Weak Convergence 324
20 Quantum Mechanics 329
1 The Static Case 329
2 The Dynamic Case 335
References 341
Index 345
|
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| discipline | Mathematik |
| edition | 4. ed. |
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| spelling | Whittle, Peter 1927-2021 Verfasser (DE-588)119218267 aut Probability via expectation Peter Whittle 4. ed. New York ; Berlin ; Heidelberg ; Barcelona ; Hong Kong ; London Springer 2000 XXI, 352 S. graph. Darst. : 24 cm txt rdacontent n rdamedia nc rdacarrier Springer texts in statistics Literaturverz. S. 341 - 344 Probabilidade larpcal Probabilités Processos de markov larpcal Processos estocasticos larpcal Waarschijnlijkheidstheorie gtt Probabilities Wahrscheinlichkeit (DE-588)4137007-7 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf 1\p (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 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009037345&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Whittle, Peter 1927-2021 Probability via expectation Probabilidade larpcal Probabilités Processos de markov larpcal Processos estocasticos larpcal Waarschijnlijkheidstheorie gtt Probabilities Wahrscheinlichkeit (DE-588)4137007-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4137007-7 (DE-588)4064324-4 (DE-588)4079013-7 (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 | Probabilidade larpcal Probabilités Processos de markov larpcal Processos estocasticos larpcal Waarschijnlijkheidstheorie gtt Probabilities Wahrscheinlichkeit (DE-588)4137007-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Probabilidade Probabilités Processos de markov Processos estocasticos Waarschijnlijkheidstheorie Probabilities Wahrscheinlichkeit Wahrscheinlichkeitsrechnung Wahrscheinlichkeitstheorie Einführung |
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