Elements of applied probability: for engineering, mathematics and systems science
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a]
World Scientific
2004
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 361 S. graph. Darst. |
| ISBN: | 9812387390 |
Internformat
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Datensatz im Suchindex
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| adam_text | ELEMENTS OF APPLIED PROBABILITY FO R ENGINEERING, MATHEMATICS AND
SYSTEMS SCIENCE DAVID MCDONALD DEPARTMENT OF MATHEMATICS AND STATISTICS
UNIVERSITY OF OTTAWA, CANADA FC WORLD SCIENTIFIC NEW JERSEY * LONDON *
SINGAPORE * SHANGHAI * HONGKONG * TAIPEI * BANGALORE CONTENTS 1.
INTRODUCTION 1 1.1 TELECOMMUNICATIONS AND QUALITY CONTROL 1 1.2 THE
DIGITAL NETWORK 1 1.3 QUALITY CONTROL 6 1.4 EXERCISES 14 1.5 A
PROBABILITY PRIMER 17 1.6 A RANDOM SAMPLE 21 1.7 JOINT DISTRIBUTIONS 25
1.8 EXERCISES 28 2. MODELLING A STOCHASTIC PROCESS 31 2.1 THE
PROBABILITY SPACE 31 2.2 RANDOM VARIABLES 38 2.3 EXPECTATION 44 2.4
CONDITIONAL PROBABILITIES 48 2.5 INDEPENDENCE 52 2.6 GENERAL RANDOM
VARIABLES 55 2.7 INDEPENDENCE OF GENERAL RANDOM VARIABLES 57 2.8 THE
KOLMOGOROV EXTENSION THEOREM 59 2.9 EXERCISES 64 3. VARIABLES AND LIMIT
THEOREMS 71 3.1 DISCRETE RANDOM VARIABLES 71 3.2 CONTINUOUS RANDOM
VARIABLES 76 3.3 GENERATING FUNCTIONS 82 XI XII ELEMENTS OF APPLIED
PROBABILITY 3.4 LAW OF LARGE NUMBERS 85 3.5 EXERCISES 92 4. THE POISSON
PROCESS 99 4.1 INTRODUCTION 99 4.2 BERNOULLI POINT PROCESSES 100 4.3 THE
POISSON PROCESS 104 4.4 APPLICATIONS OF THE POISSON PROCESS 107 4.5 A
FURTHER CHARACTERIZATION 110 4.6 THE POISSON APPROXIMATION 113 4.7
NONHOMOGENEOUS POISSON PROCESSES 119 4.8 EXERCISES 123 5. MARKOV CHAINS
127 5.1 INTRODUCTION 127 5.2 STEADY-STATE MARKOV CHAINS 135 5.3
CONVERGENCE TO STEADY-STATE 140 5.4 REVERSIBLE MARKOV CHAINS 147 5.5
HITTING PROBABILITIES 150 5.6 PROOFS OF CONVERGENCE TO STEADY STATE 161
5.7 TRANSIENCE AND RECURRENCE 165 5.8 EXISTENCE AND THE STRONG MARKOV
PROPERTY 169 5.9 THE WATCHED PROCESS 171 5.10 FOSTER S CRITERION FOR
STABILITY 175 5.11 EXERCISES 177 6. RENEWAL THEORY 183 6.1 INTRODUCTION
183 6.2 RENEWAL REWARD PROCESSES 187 6.3 STATIONARY RENEWAL PROCESSES
192 6.4 CONVERGENCE TO STATIONARITY 203 6.5 RENEWAL WITH NONLATTICE
VARIABLES 209 6.6 HOMOGENEOUS COUPLING 210 6.7 THE BERNOULLI PART AND
COUPLING 214 6.8 PROOF OF THE COUPLING THEOREM 217 6.9 REGENERATIVE
PROCESSES 221 6.10 EXERCISES 225 7. MARKOV PROCESSES 229 7.1
INTRODUCTION 229 7.2 THE GENERATOR OF A MARKOV PROCESS 231 7.3 QUEUES
AND TIME REVERSAL 242 CONTENTS XIII 7.4 JACKSON NETWORKS 250 7.5 KELLY
OR BCMP NETWORKS 254 7.6 APPROXIMATION BY A MARKOV PROCESS 261 7.7
EXERCISES 265 8. MARKOV DECISION THEORY 271 8.1 INTRODUCTION 271 8.2 THE
OPTIMALITY EQUATION 276 8.3 INFINITE HORIZON DECISION PROBLEMS 286 8.4
CONTINUOUS TIME DECISION PROBLEMS 295 8.5 OPTIMAL STOPPING 298 8.6
QUALITY CONTROL - A WORST CASE ANALYSIS 308 8.7 EXERCISES 314 9.
APPENDIX 319 9.1 USEFUL RESULTS IN ANALYSIS 319 9.2 INTEGRATION AND
EXPECTATION 319 9.3 CONVEXITY 322 9.4 NORMS AND FIXED POINTS 324 9.5
ALGEBRAIC RESULTS 327 9.6 FURTHER READING 328 9.7 BIBLIOGRAPHY 330 9.8
SOLUTIONS TO SELECTED PROBLEMS 334 9.8.1 SOLUTIONS TO SELECTED EXERCISES
IN CHAPTER 1 334 9.8.2 SOLUTIONS TO SELECTED EXERCISES IN CHAPTER 2 336
9.8.3 SOLUTIONS TO SELECTED EXERCISES IN CHAPTER 3 338 9.8.4 SOLUTIONS
TO SELECTED EXERCISES IN CHAPTER 4 342 9.8.5 SOLUTIONS TO SELECTED
EXERCISES IN CHAPTER 5 346 9.8.6 SOLUTIONS TO SELECTED EXERCISES IN
CHAPTER 6 349 9.8.7 SOLUTIONS TO SELECTED EXERCISES IN CHAPTER 7 352
9.8.8 SOLUTIONS TO SELECTED EXERCISES IN CHAPTER 8 354 INDEX 359
|
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| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| isbn | 9812387390 |
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| spelling | McDonald, David R. Verfasser aut Elements of applied probability for engineering, mathematics and systems science David McDonald Singapore [u.a] World Scientific 2004 XIII, 361 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017437672&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | McDonald, David R. Elements of applied probability for engineering, mathematics and systems science Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4064324-4 |
| title | Elements of applied probability for engineering, mathematics and systems science |
| title_auth | Elements of applied probability for engineering, mathematics and systems science |
| title_exact_search | Elements of applied probability for engineering, mathematics and systems science |
| title_full | Elements of applied probability for engineering, mathematics and systems science David McDonald |
| title_fullStr | Elements of applied probability for engineering, mathematics and systems science David McDonald |
| title_full_unstemmed | Elements of applied probability for engineering, mathematics and systems science David McDonald |
| title_short | Elements of applied probability |
| title_sort | elements of applied probability for engineering mathematics and systems science |
| title_sub | for engineering, mathematics and systems science |
| topic | Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Wahrscheinlichkeitsrechnung |
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