Applied probability and stochastic processes:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2010
|
| Edition: | 2. Aufl. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | XV, 397 S. Ill., graph. Darst. |
| ISBN: | 9783642051555 |
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Record in the Search Index
| _version_ | 1804143158921003008 |
|---|---|
| adam_text | IMAGE 1
APPLIED PROBABILITY AND STOCHASTIC PROCESSES
SECOND EDITION
IMAGE 2
CONTENTS
1 BASIC PROBABILITY REVIEW 1
1 . 1 BASIC DEFINITIONS 1
1.2 RANDOM VARIABLES AND DISTRIBUTION FUNCTIONS 4
1.3 MEAN AND VARIANCE 10
1.4 IMPORTANT DISTRIBUTIONS 13
1.5 MULTIVARIATE DISTRIBUTIONS 23
1.6 COMBINATIONS OF RANDOM VARIABLES 31
1.6.1 FIXED SUM OF RANDOM VARIABLES 32
1.6.2 RANDOM SUM OF RANDOM VARIABLES 32
1.6.3 MIXTURES OF RANDOM VARIABLES 34
APPENDIX 35
PROBLEMS 37
REFERENCES 43
2 BASICS OF MONTE CARLO SIMULATION 45
2.1 SIMULATION BY HAND 46
2.2 GENERATION OF RANDOM NUMBERS 49
2.2.1 MULTIPLICATIVE LINEAR CONGRUENTIAL GENERATORS 50 2.2.2 A MULTIPLE
RECURSIVE GENERATOR 52
2.2.3 COMPOSITE GENERATORS 53
2.3 GENERATION OF RANDOM VARIATES 55
2.3.1 DISCRETE RANDOM VARIATES 55
2.3.2 CONTINUOUS RANDOM VARIATES 61
2.3.3 BIVARIATE CONTINUOUS RANDOM VARIATES 64
2.3.4 RANDOM VARIATES FROM EMPIRICAL DISTRIBUTIONS 66 APPENDIX 67
PROBLEMS 69
REFERENCES 72
IMAGE 3
CONTENTS
BASIC STATISTICAL REVIEW 73
3.1 COLLECTION OF DATA 73
3.1.1 PRELIMINARY DEFINITIONS 74
3.1.2 GRAPHICAL REPRESENTATIONS 75
3.2 PARAMETER ESTIMATION 78
3.2.1 METHOD OF MOMENTS 80
3.2.2 MAXIMUM LIKELIHOOD ESTIMATION 81
3.3 CONFIDENCE INTERVALS 82
3.3.1 MEANS 83
3.3.2 PROPORTIONS 87
3.3.3 VARIANCES 87
3.3.4 CORRELATION COEFFICIENT 89
3.4 FITTING DISTRIBUTIONS 90
3.4.1 THE CHI-SQUARE TEST 91
3.4.2 THE KOLMOGOROV-SMIRNOV TEST 95
3.5 FITTING MODELS 99
3.5.1 ORDINARY LEAST SQUARES REGRESSION 100
3.5.2 MAXIMUM LIKELIHOOD ESTIMATES FOR LINEAR MODELS 105 APPENDIX 105
PROBLEMS 109
REFERENCES 113
POISSON PROCESSES 115
4.1 BASIC DEFINITIONS 115
4.2 PROPERTIES AND COMPUTATIONS 118
4.3 EXTENSIONS OF A POISSON PROCESS 121
4.3.1 COMPOUND POISSON PROCESSES 121
4.3.2 NON-STATIONARY POISSON PROCESS 123
4.4 POISSON REGRESSION 124
4.4.1 POISSON REGRESSION WITH ONE INDEPENDENT VARIABLE 124 4.4.2 POISSON
REGRESSION WITH SEVERAL INDEPENDENT VARIABLES . . .. 128 APPENDIX 133
PROBLEMS 136
REFERENCES 139
MARKOV CHAINS 141
5.1 BASIC DEFINITIONS 142
5.2 MULTISTEP TRANSITIONS 145
5.3 CLASSIFICATION OF STATES 149
5.4 STEADY-STATE BEHAVIOR 157
5.5 COMPUTATIONS 162
APPENDIX 169
PROBLEMS 171
REFERENCES 178
IMAGE 4
CONTENTS XIII
6 MARKOV PROCESSES 181
6. 1 BASIC DEFINITIONS 181
6.2 STEADY-STATE PROPERTIES 184
6.3 REVENUES AND COSTS 188
6.4 TIME-DEPENDENT PROBABILITIES 191
APPENDIX 195
PROBLEMS 196
7 QUEUEING PROCESSES 201
7.1 BASIC DEFINITIONS AND NOTATION 201
7.2 SINGLE SERVER SYSTEMS 203
7.2.1 INFINITE CAPACITY SINGLE-SERVER SYSTEMS 203
7.2.2 FINITE CAPACITY SINGLE SERVER SYSTEMS 210
7.3 MULTIPLE SERVER QUEUES 213
7.4 APPROXIMATIONS 217
APPENDIX 219
PROBLEMS 220
REFERENCES 225
8 QUEUEING NETWORKS 227
8.1 JACKSON NETWORKS 227
8.1.1 OPEN JACKSON NETWORKS 228
8.1.2 CLOSED JACKSON NETWORKS 232
8.2 NETWORK APPROXIMATIONS 235
8.2.1 DETERMINISTIC ROUTING WITH POISSON INPUT 236
8.2.2 DETERMINISTIC ROUTING WITH NON-POISSON INPUT 242 APPENDIX 245
PROBLEMS 246
REFERENCES 249
9 EVENT-DRIVEN SIMULATION AND OUTPUT ANALYSES 251
9.1 EVENT-DRIVEN SIMULATIONS 251
9.2 STATISTICAL ANALYSIS OF OUTPUT 262
9.2.1 TERMINATING SIMULATIONS 263
9.2.2 STEADY-STATE SIMULATIONS 266
9.2.3 COMPARING SYSTEMS 275
PROBLEMS - S . 279
REFERENCES 284
10 INVENTORY THEORY 285
10.1 THE NEWS-VENDOR PROBLEM 286
10.2 SINGLE-PERIOD INVENTORY 289
10.2.1 NO SETUP COSTS 289
10.2.2 SETUP COSTS 292
10.3 MULTI-PERIOD INVENTORY 295
IMAGE 5
XIV CONTENTS
PROBLEMS 299
REFERENCES 303
11 REPLACEMENT THEORY 305
11.1 AGE REPLACEMENT 305
11.1.1 DISCRETE LIFE TIMES 306
11.1.2 CONTINUOUS LIFE TIMES 309
11.2 MINIMAL REPAIR 312
11.2.1 MINIMAL REPAIRS WITHOUT EARLY REPLACEMENTS 313 11.2.2 MINIMAL
REPAIRS WITH EARLY REPLACEMENTS 314
11.3 BLOCK REPLACEMENT 316
PROBLEMS 319
12 MARKOV DECISION PROCESSES 323
--. 12.1 BASIC DEFINITIONS 324
12.1.1 EXPECTED TOTAL DISCOUNTED COST CRITERION 326
12.1.2 AVERAGE LONG-RUN COST CRITERION 327
12.2 STATIONARY POLICIES 327
12.3 DISCOUNTED COST ALGORITHMS 329
12.3.1 VALUE IMPROVEMENT FOR DISCOUNTED COSTS 331
12.3.2 POLICY IMPROVEMENT FOR DISCOUNTED COSTS 332
12.3.3 LINEAR PROGRAMMING FOR DISCOUNTED COSTS 336
12.4 AVERAGE COST ALGORITHMS 337
12.4.1 POLICY IMPROVEMENT FOR AVERAGE COSTS 340
12.4.2 LINEAR PROGRAMMING FOR AVERAGE COSTS 344
12.5 THE OPTIMAL STOPPING PROBLEM 346
PROBLEMS 349
13 ADVANCED QUEUES 355
1 3.1 DIFFERENCE EQUATIONS 356
13.2 BATCH ARRIVALS 358
13.2.1 QUASI-BIRTH-DEATH PROCESSES 360
13.2.2 BATCH ARRIVALS (CONTINUED) 362
13.3 PHASE-TYPE DISTRIBUTIONS 364
13.4 SYSTEMS WITH PHASE-TYPE SERVICE 368
13.4.1 THE M/PH/1 QUEUEING SYSTEM 368
13.4.2 THE M/PH/C QUEUEING SYSTEM 372
13.5 SYSTEMS WITH PHASE-TYPE ARRIVALS 374
PROBLEMS * . .. 375
REFERENCES 379
A MATRIX REVIEW 381
A. 1 MATRIX ADDITION AND SUBTRACTION 382
A.2 MATRIX MULTIPLICATION 382
A.3 DETERMINANTS 383
A.4 DETERMINANTS BY COFACTOR EXPANSION 385
IMAGE 6
CONTENTS XV
A.5 NONSINGULAR MATRICES 386
A.6 INVERSION-IN-PLACE 387
A.7- DERIVATIVES 390
REFERENCES 392
INDEX 393
|
| any_adam_object | 1 |
| author | Feldman, Richard M. Valdez-Flores, Ciriaco |
| author_facet | Feldman, Richard M. Valdez-Flores, Ciriaco |
| author_role | aut aut |
| author_sort | Feldman, Richard M. |
| author_variant | r m f rm rmf c v f cvf |
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| bvnumber | BV036574918 |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)699285255 (DE-599)DNB996813292 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| 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 |
| edition | 2. Aufl. |
| format | Book |
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| isbn | 9783642051555 |
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| spelling | Feldman, Richard M. Verfasser aut Applied probability and stochastic processes Richard M. Feldman ; Ciriaco Valdez-Flores 2. Aufl. Berlin [u.a.] Springer 2010 XV, 397 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Stochastischer Prozess (DE-588)4057630-9 s Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s DE-604 Valdez-Flores, Ciriaco Verfasser aut Erscheint auch als Online-Ausgabe 978-3-642-05158-6 DE-601 pdf/application http://www.gbv.de/dms/zbw/609423665.pdf kostenfrei Inhaltsverzeichnis GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020495943&sequence=000001&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 | Feldman, Richard M. Valdez-Flores, Ciriaco Applied probability and stochastic processes Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)4057630-9 (DE-588)4123623-3 |
| title | Applied probability and stochastic processes |
| title_auth | Applied probability and stochastic processes |
| title_exact_search | Applied probability and stochastic processes |
| title_full | Applied probability and stochastic processes Richard M. Feldman ; Ciriaco Valdez-Flores |
| title_fullStr | Applied probability and stochastic processes Richard M. Feldman ; Ciriaco Valdez-Flores |
| title_full_unstemmed | Applied probability and stochastic processes Richard M. Feldman ; Ciriaco Valdez-Flores |
| title_short | Applied probability and stochastic processes |
| title_sort | applied probability and stochastic processes |
| topic | Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Wahrscheinlichkeitsrechnung Stochastischer Prozess Lehrbuch |
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