Stochastic processes an introduction
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2010
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Chapman & Hall/CRC texts in statistical science series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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MARC
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| 245 | 1 | 0 | |a Stochastic processes |b an introduction |c Peter W. Jones ; Peter Smith |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2010 | |
| 300 | |a X, 221 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Chapman & Hall/CRC texts in statistical science series | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Stochastic processes | |
| 650 | 0 | 7 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| DE-BY-862_location | 2000 |
|---|---|
| DE-BY-FWS_call_number | 2000/SK 820 J78(2) |
| DE-BY-FWS_katkey | 389132 |
| DE-BY-FWS_media_number | 083000502554 |
| _version_ | 1806174571587436544 |
| adam_text | IMAGE 1
CONTENTS
PREFACE IX
1 SOME BACKGROUND ON PROBABILITY 1
1.1 INTRODUCTION 1
1.2 PROBABILITY 1
1.3 CONDITIONAL PROBABILITY AND INDEPENDENCE 5
1.4 DISCRETE RANDOM VARIABLES 7
1.5 CONTINUOUS RANDOM VARIABLES 9
1.6 MEAN AND VARIANCE 10
1.7 SOME STANDARD DISCRETE PROBABILITY DISTRIBUTIONS 12
1.8 SOME STANDARD CONTINUOUS PROBABILITY DISTRIBUTIONS 14
1.9 GENERATING FUNCTIONS 17
1.10 CONDITIONAL EXPECTATION 21
1.11 PROBLEMS 24
2 SOME GAMBLING PROBLEMS 29
2.1 GAMBLER S RUIN 29
2.2 PROBABILITY OF RUIN 29
2.3 SOME NUMERICAL SIMULATIONS 33
2.4 DURATION OF THE GAME 34
2.5 SOME VARIATIONS OF GAMBLER S RUIN 38
2.5.1 THE INFINITELY RICH OPPONENT 38
2.5.2 THE GENEROUS OPPONENT 38
2.5.3 CHANGING THE STAKES 39
2.6 PROBLEMS 39
3 RANDOM WALKS 45
3.1 INTRODUCTION 45
3.2 UNRESTRICTED RANDOM WALKS 46
3.3 THE GENERAL PROBABILITY DISTRIBUTION OF A WALK 48
3.4 FIRST RETURNS OF THE SYMMETRIC RANDOM WALK 50
3.5 PROBLEMS 52
4 MARKOV CHAINS 59
4.1 STATES AND TRANSITIONS 59
4.2 TRANSITION PROBABILITIES 60
IMAGE 2
4.3 GENERAL TWO-STATE MARKOV CHAINS 64
4.4 POWERS OF THE GENERAL TRANSITION MATRIX 66
4.5 GAMBLER S RUIN AS A MARKOV CHAIN 73
4.6 CLASSIFICATION OF STATES 76
4.7 CLASSIFICATION OF CHAINS 83
4.8 PROBLEMS 86
5 POISSON PROCESSES 93
5.1 INTRODUCTION 93
5.2 THE POISSON PROCESS 93
5.3 PARTITION THEOREM APPROACH 96
5.4 ITERATIVE METHOD 97
5.5 THE GENERATING FUNCTION 98
5.6 VARIANCE IN TERMS OF THE PROBABILITY GENERATING FUNCTION 100 5.7
ARRIVAL TIMES 101
5.8 SUMMARY OF THE POISSON PROCESS 103
5.9 PROBLEMS 104
6 BIRTH AND DEATH PROCESSES 107
6.1 INTRODUCTION 107
6.2 THE BIRTH PROCESS 107
6.3 BIRTH PROCESS: GENERATING FUNCTION EQUATION 110
6.4 THE DEATH PROCESS 112
6.5 THE COMBINED BIRTH AND DEATH PROCESS 115
6.6 GENERAL POPULATION PROCESSES 119
6.7 PROBLEMS 122
7 QUEUES 131
7.1 INTRODUCTION 131
7.2 THE SINGLE-SERVER QUEUE 132
7.3 THE STATIONARY PROCESS 134
7.4 QUEUES WITH MULTIPLE SERVERS 140
7.5 QUEUES WITH FIXED SERVICE TIMES 144
7.6 CLASSIFICATION OF QUEUES 147
7.7 A GENERAL APPROACH TO THE M(X)/G/1 QUEUE 147
7.8 PROBLEMS 151
8 RELIABILITY AND RENEWAL 157
8.1 INTRODUCTION 157
8.2 THE RELIABILITY FUNCTION 157
8.3 EXPONENTIAL DISTRIBUTION AND RELIABILITY 159
8.4 MEAN TIME TO FAILURE 160
8.5 RELIABILITY OF SERIES AND PARALLEL SYSTEMS 161
8.6 RENEWAL PROCESSES 163
8.7 EXPECTED NUMBER OF RENEWALS 165
IMAGE 3
8.8 PROBLEMS 167
9 BRANCHING AND OTHER RANDOM PROCESSES 171
9.1 INTRODUCTION 171
9.2 GENERATIONAL GROWTH 171
9.3 MEAN AND VARIANCE 174
9.4 PROBABILITY OF EXTINCTION 176
9.5 BRANCHING PROCESSES AND MARTINGALES 179
9.6 STOPPING RULES 182
9.7 THE SIMPLE EPIDEMIC 184
9.8 AN ITERATIVE SOLUTION SCHEME FOR THE SIMPLE EPIDEMIC 186
9.9 PROBLEMS 188
10 COMPUTER SIMULATIONS AND PROJECTS 195
ANSWERS AND COMMENTS ON END-OF-CHAPTER PROBLEMS 203
APPENDIX 211
REFERENCES AND FURTHER READING 215
INDEX 217
|
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| author | Jones, Peter Watts 1945- |
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| ctrlnum | (OCoLC)429816920 (DE-599)BVBBV036097619 |
| dewey-full | 519.2/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/3 |
| dewey-search | 519.2/3 |
| dewey-sort | 3519.2 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-08-01T10:51:39Z |
| institution | BVB |
| isbn | 9781420099607 |
| language | English |
| lccn | 2009031438 |
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| physical | X, 221 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Chapman & Hall/CRC |
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| series2 | Chapman & Hall/CRC texts in statistical science series |
| spellingShingle | Jones, Peter Watts 1945- Stochastic processes an introduction Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4057630-9 |
| title | Stochastic processes an introduction |
| title_auth | Stochastic processes an introduction |
| title_exact_search | Stochastic processes an introduction |
| title_full | Stochastic processes an introduction Peter W. Jones ; Peter Smith |
| title_fullStr | Stochastic processes an introduction Peter W. Jones ; Peter Smith |
| title_full_unstemmed | Stochastic processes an introduction Peter W. Jones ; Peter Smith |
| title_short | Stochastic processes |
| title_sort | stochastic processes an introduction |
| title_sub | an introduction |
| topic | Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Stochastic processes Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018988076&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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