Introduction to stochastic models
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Menlo Park, Calif.
Benjamin/Cummings
1988
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Goodman, Roe |d 1938- |e Verfasser |0 (DE-588)123134943 |4 aut | |
| 245 | 1 | 0 | |a Introduction to stochastic models |
| 264 | 1 | |a Menlo Park, Calif. |b Benjamin/Cummings |c 1988 | |
| 300 | |a XII, 368 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Probabilités | |
| 650 | 4 | |a Processus stochastiques - Modèles mathématiques | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Probabilities | |
| 650 | 4 | |a Stochastic processes |x Mathematical models | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102/MAT 605f 2001 A 15866 0102/MAT 605f 2001 A 15867 |
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| DE-BY-TUM_media_number | 040010613099 040010613088 |
| _version_ | 1816711374924939264 |
| adam_text | Contents
Chapter 1 Sample Spaces 1
Introduction 1
1.1 Experiments with Random Outcomes 1
1.2 Sample Spaces, Events, and Random Variables 3
Exercises 6
Chapter 2 Probabilities 7
Introduction 7
2.1 Relative Frequency of Events 7
2.2 Axioms of Probability 13
2.3 Conditional Probability and Bayes Formula 24
2.4 Stochastic Independence 29
2.5 Repeated Independent Trials 32
Exercises 40
Chapter 3 Distributions and Expectations of Random
Variables 45
Introduction 45
3.1 Distribution Function of a Random Variable 45
3.2 Discrete Random Variables 47
3.3 Continuous Random Variables 52
3.4 Expectation of a Random Variable 57
ix
Contents
3.5 Functions of a Random Variable 61
3.6 Simulation of a Random Variable 66
Exercises 71
Chapter 4 Joint Distributions of Random Variables 75
Introduction 75
4.1 Joint Mass Functions and Densities 75
4.2 Independent Random Variables 82
4.3 Moment generating Functions 89
4.4 Families of Random Variables 92
4.5 Markov and Chebyshev Inequalities 95
4.6 Law of Large Numbers 98
4.7 Central Limit Theorem 102
Exercises 108
Chapter 5 Conditional Expectations 113
Introduction 113
5.1 Conditional Distributions (Discrete Case) 113
5.2 Conditional Expectations 115
5.3 Conditional Expectations (Continuous Case) 118
5.4 Sum of a Random Number of Random Variables 122
Exercises 124
Chapter 6 Markov Chains 127
Introduction 127
6.1 State Spaces and Transition Diagrams 127
6.2 Joint Probabilities 133
6.3 More Examples 139
6.4 « Step Transition Probabilities 146
6.5 Classification of States 151
6.6 Absorbing Chains 157
6.7 Regular Chains 164
6.8 Stationary Distributions 169
6.9 Time Averages 172
6.10 Sojourn Times and First Entrance Times 176
Exercises 182
Contents
Chapter 7 The Poisson Process 187
Introduction 187
7.1 Memoryless Random Variables 187
7.2 Replacement Models 193
7.3 Simulation of a Poisson Process 194
7.4 Fundamental Properties of a Poisson Process 196
7.5 Differential Equations for a Poisson Process 200
Exercises 203
Chapter 8 Continuous Time Stochastic Processes 207
Introduction 207
8.1 Stochastic Processes 207
8.2 Characterization of the Poisson Process 209
8.3 Discrete Time Approximation to the Poisson Process 213
8.4 Compound Poisson Process 215
8.5 Nonhomogeneous Poisson Process 218
8.6 Queueing Processes 221
8.7 M/M/l Queue and Exponential Models 224
Exercises 227
Chapter 9 Birth and Death Processes 231
Introduction 231
9.1 Linear Growth Model 231
9.2 Birth Death Processes 232
9.3 State Transition Diagrams 234
9.4 Transition Probabilities 237
9.5 Differential Equations for Transition Probabilities 241
9.6 Pure Birth Processes 245
Exercises 247
Chapter 10 Steady State Probabilities 251
Introduction 251
10.1 Approach to Equilibrium 251
10.2 Steady State Equations 252
10.3 Limiting Probabilities 254
10.4 Balance Equations 258
Contents
10.5 Time Averages 260
10.6 Steady State Analysis of the M/M/l Queue 264
10.7 Machine Repair Model 266
Exercises 267
Chapter 11 General Queueing Systems 271
Introduction 271
11.1 Long Term Average Queue Characteristics 272
11.2 Little s Formula 274
11.3 Steady State Behavior of M/M/l Queue 275
11.4 Service in Stages 278
11.5 Jackson s Theorem 282
11.6 M/M/s Queue Statistics 284
11.7 Optimization Problems 291
11.8 Examples of Queue Simulation 296
Exercises 305
Chapter 12 Renewal Processes 313
Introduction 313
12.1 Failure Rates 314
12.2 Renewal Model 317
12.3 Random Stopping Rules and Wald s Identity 321
12.4 Renewals with Rewards 324
12.5 Age Replacement Model 328
12.6 Regeneration Points 332
12.7 Lifetime Sampling and the Inspection Paradox 338
12.8 Waiting Times for the M/G/l Queue 343
Exercises 346
Table 1. Discrete Probability Distributions 352
Table 2. Continuous Probability Distributions 353
Table 3. Cumulative Normal Distribution Function 354
Table 4. Random Numbers 355
Suggestions for Further Reading 356
Numerical Solutions to Selected Exercises 358
Index 364
|
| any_adam_object | 1 |
| author | Goodman, Roe 1938- |
| author_GND | (DE-588)123134943 |
| author_facet | Goodman, Roe 1938- |
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| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| genre | 1\p (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV002065687 |
| illustrated | Illustrated |
| indexdate | 2024-11-25T17:07:22Z |
| institution | BVB |
| isbn | 0805360115 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001350859 |
| oclc_num | 16756307 |
| open_access_boolean | |
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| owner_facet | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-739 DE-706 DE-83 DE-188 |
| physical | XII, 368 S. graph. Darst. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Benjamin/Cummings |
| record_format | marc |
| spellingShingle | Goodman, Roe 1938- Introduction to stochastic models Probabilités Processus stochastiques - Modèles mathématiques Mathematisches Modell Probabilities Stochastic processes Mathematical models Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)4057630-9 (DE-588)4057633-4 (DE-588)4123623-3 |
| title | Introduction to stochastic models |
| title_auth | Introduction to stochastic models |
| title_exact_search | Introduction to stochastic models |
| title_full | Introduction to stochastic models |
| title_fullStr | Introduction to stochastic models |
| title_full_unstemmed | Introduction to stochastic models |
| title_short | Introduction to stochastic models |
| title_sort | introduction to stochastic models |
| topic | Probabilités Processus stochastiques - Modèles mathématiques Mathematisches Modell Probabilities Stochastic processes Mathematical models Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| topic_facet | Probabilités Processus stochastiques - Modèles mathématiques Mathematisches Modell Probabilities Stochastic processes Mathematical models Wahrscheinlichkeitsrechnung Stochastischer Prozess Stochastisches Modell Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001350859&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT goodmanroe introductiontostochasticmodels |