Stochastic processes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Wiley
1996
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Wiley series in probability and mathematical statistics
|
| Schlagworte: | |
| Online-Zugang: | Publisher description Table of Contents Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XV, 510 S. graph. Darst. |
| ISBN: | 0471120626 |
Internformat
MARC
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| 100 | 1 | |a Ross, Sheldon M. |d 1943- |e Verfasser |0 (DE-588)123762235 |4 aut | |
| 245 | 1 | 0 | |a Stochastic processes |c Sheldon M. Ross |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY [u.a.] |b Wiley |c 1996 | |
| 300 | |a XV, 510 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley series in probability and mathematical statistics | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Stochastic processes | |
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Datensatz im Suchindex
| _version_ | 1804125325602324480 |
|---|---|
| adam_text | Contents
CHAPTER 1. PRELIMINARIES 1
1.1. Probability 1
1.2. Random Variables 7
1.3. Expected Value 9
1.4. Moment Generating, Characteristic Functions, and
Laplace Transforms 15
1.5. Conditional Expectation 20
1.5.1. Conditional Expectations and Bayes
Estimators 33
1.6. The Exponential Distribution, Lack of Memory, and
Hazard Rate Functions 35
1.7. Some Probability Inequalities 39
1.8. Limit Theorems 41
1.9. Stochastic Processes 41
Problems 46
References 55
Appendix 56
CHAPTER 2. THE POISSON PROCESS 59
2.1. The Poisson Process 59
2.2. Interarrival and Waiting Time Distributions 64
2.3. Conditional Distribution of the Arrival Times 66
2.3.1. The M/G/l Busy Period 73
2.4. Nonhomogeneous Poisson Process 78
2.5. Compound Poisson Random Variables and
Processes 82
2.5.1. A Compound Poisson Identity 84
2.5.2. Compound Poisson Processes 87
id
Xii CONTENTS
2.6. Conditional Poisson Processes 88
Problems 89
References 97
CHAPTER 3. RENEWAL THEORY 98
3.1. Introduction and Preliminaries 98
3.2. Distribution of N(t) 99
3.3. Some Limit Theorems 101
3.3.1. Wald s Equation 104
3.3.2. Back to Renewal Theory 106
3.4. The Key Renewal Theorem and Applications 109
3.4.1. Alternating Renewal Processes 114
3.4.2. Limiting Mean Excess and Expansion
of m{t) 119
3.4.3. Age Dependent Branching Processes 121
3.5. Delayed Renewal Processes 123
3.6. Renewal Reward Processes 132
3.6.1. A Queueing Application 138
3.7. Regenerative Processes 140
3.7.1. The Symmetric Random Walk and the Arc Sine
Laws 142
3.8. Stationary Point Processes 149
Problems 153
References 161
CHAPTER 4. MARKOV CHAINS 163
4.1. Introduction and Examples 163
4.2. Chapman Kolmogorov Equations and Classification of
States 167
4.3. Limit Theorems 173
4.4. Transitions among Classes, the Gambler s Ruin Problem,
and Mean Times in Transient States 185
4.5. Branching Processes 191
4.6. Applications of Markov Chains 193
4.6.1. A Markov Chain Model of Algorithmic
Efficiency 193
4.6.2. An Application to Runs—A Markov Chain with a
Continuous State Space 195
4.6.3. List Ordering Rules—Optimality of the
Transposition Rule 198
CONTENTS Xili
4.7. Time Reversible Markov Chains 203
4.8. Semi Markov Processes 213
Problems 219
References 230
CHAPTER 5. CONTINUOUS TIME MARKOV CHAINS 231
5.1. Introduction 231
5.2. Continuous Time Markov Chains 231
5.3. Birth and Death Processes 233
5.4. The Kolmogorov Differential Equations 239
5.4.1. Computing the Transition Probabilities 249
5.5. Limiting Probabilities 251
5.6. Time Reversibility 257
5.6.1. Tandem Queues 262
5.6.2. A Stochastic Population Model 263
5.7. Applications of the Reversed Chain to Queueing
Theory 270
5.7.1. Network of Queues 271
5.7.2. The Erlang Loss Formula 275
5.7.3. The M/G/l Shared Processor System 278
5.8. Uniformization 282
Problems 286
References 294
CHAPTER 6. MARTINGALES 295
Introduction 295
6.1. Martingales 295
6.2. Stopping Times 298
6.3. Azuma s Inequality for Martingales 305
6.4. Submartingales, Supermartingales, and the Martingale
Convergence Theorem 313
6.5. A Generalized Azuma Inequality 319
Problems 322
References 327
CHAPTER 7. RANDOM WALKS 328
Introduction 328
7.1. Duality in Random Walks 329
xiv CONTENTS
7.2. Some Remarks Concerning Exchangeable Random
Variables 338
7.3. Using Martingales to Analyze Random Walks 341
7.4. Applications to GIG/1 Queues and Ruin
Problems 344
7.4.1. The G/G/l Queue 344
7.4.2. A Ruin Problem 347
7.5. Blackwell s Theorem on the Line 349
Problems 352
References 355
CHAPTER 8. BROWNIAN MOTION AND OTHER MARKOV
PROCESSES 356
8.1. Introduction and Preliminaries 356
8.2. Hitting Times, Maximum Variable, and Arc Sine
Laws 363
8.3. Variations on Brownian Motion 366
8.3.1. Brownian Motion Absorbed at a Value 366
8.3.2. Brownian Motion Reflected at the Origin 368
8.3.3. Geometric Brownian Motion 368
8.3.4. Integrated Brownian Motion 369
8.4. Brownian Motion with Drift 372
8.4.1. Using Martingales to Analyze Brownian
Motion 381
8.5. Backward and Forward Diffusion Equations 383
8.6. Applications of the Kolmogorov Equations to Obtaining
Limiting Distributions 385
8.6.1. Semi Markov Processes 385
8.6.2. The Ml Gil Queue 388
8.6.3. A Ruin Problem in Risk Theory 392
8.7. A Markov Shot Noise Process 393
8.8. Stationary Processes 396
Problems 399
References 403
CHAPTER 9. STOCHASTIC ORDER RELATIONS 404
Introduction 404
9.1. Stochastically Larger 404
CONTENTS XV
9.2. Coupling 409
9.2.1. Stochastic Monotonicity Properties of Birth and
Death Processes 416
9.2.2. Exponential Convergence in Markov
Chains 418
9.3. Hazard Rate Ordering and Applications to Counting
Processes 420
9.4. Likelihood Ratio Ordering 428
9.5. Stochastically More Variable 433
9.6. Applications of Variability Orderings 437
9.6.1. Comparison of G/G/l Queues 439
9.6.2. A Renewal Process Application 440
9.6.3. A Branching Process Application 443
9.7. Associated Random Variables 446
Problems 449
References 456
CHAPTER 10. POISSON APPROXIMATIONS 457
Introduction 457
10.1. Brun s Sieve 457
10.2. The Stein Chen Method for Bounding the Error of the
Poisson Approximation 462
10.3. Improving the Poisson Approximation 467
Problems 470
References 472
ANSWERS AND SOLUTIONS TO SELECTED PROBLEMS 473
INDEX SOS
|
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| discipline | Biologie Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
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| id | DE-604.BV010838123 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:59:46Z |
| institution | BVB |
| isbn | 0471120626 |
| language | English |
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| physical | XV, 510 S. graph. Darst. |
| publishDate | 1996 |
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| series2 | Wiley series in probability and mathematical statistics |
| spelling | Ross, Sheldon M. 1943- Verfasser (DE-588)123762235 aut Stochastic processes Sheldon M. Ross 2. ed. New York, NY [u.a.] Wiley 1996 XV, 510 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and mathematical statistics Hier auch später erschienene, unveränderte Nachdrucke Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s DE-604 http://www.loc.gov/catdir/description/wiley033/95038012.html Publisher description http://www.loc.gov/catdir/toc/onix04/95038012.html Table of Contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007244772&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ross, Sheldon M. 1943- Stochastic processes Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4057630-9 |
| title | Stochastic processes |
| title_auth | Stochastic processes |
| title_exact_search | Stochastic processes |
| title_full | Stochastic processes Sheldon M. Ross |
| title_fullStr | Stochastic processes Sheldon M. Ross |
| title_full_unstemmed | Stochastic processes Sheldon M. Ross |
| title_short | Stochastic processes |
| title_sort | stochastic processes |
| topic | Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Stochastic processes Stochastischer Prozess |
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