Ross Introduction to Probability Models

5. Auflage 2014
ISBN: 978-1-4832-7658-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 568 Seiten, Web PDF

Introduction to Probability Models, Fifth Edition focuses on different probability models of natural phenomena. This edition includes additional material in Chapters 5 and 10, such as examples relating to analyzing algorithms, minimizing highway encounters, collecting coupons, and tracking the AIDS virus. The arbitrage theorem and its relationship to the duality theorem of linear program are also covered, as well as how the arbitrage theorem leads to the Black-Scholes option pricing formula. Other topics include the Bernoulli random variable, Chapman-Kolmogorov equations, and properties of the exponential distribution. The continuous-time Markov chains, single-server exponential queueing system, variations on Brownian motion; and variance reduction by conditioning are also elaborated. This book is a good reference for students and researchers conducting work on probability models.

Autoren/Hrsg.

Ross, Sheldon M.

Inhaltsverzeichnis

1;Front Cover;1
2;Introduction to Probability Models;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;12
6;Chapter 1. Introduction to Probability Theory;14
6.1;1.1. Introduction;14
6.2;1.2. Sample Space and Events;14
6.3;1.3. Probabilities Defined on Events;17
6.4;1.4. Conditional Probabilities;20
6.5;1.5. Independent Events;23
6.6;1.6. Bayes' Formula;25
6.7;Exercises;28
6.8;References;33
7;Chapter 2. Random Variables;34
7.1;2.1. Random Variables;34
7.2;2.2. Discrete Random Variables;38
7.3;2.3. Continuous Random Variables;44
7.4;2.4. Expectation of a Random Variable;49
7.5;2.5. Jointly Distributed Random Variables;57
7.6;2.6. Moment Generating Functions;71
7.7;2.7. Limit Theorems;79
7.8;2.8. Stochastic Processes;83
7.9;Exercises;85
7.10;References;95
8;Chapter 3. Conditional Probability and Conditional Expectation;96
8.1;3.1. Introduction;96
8.2;3.2. The Discrete Case;96
8.3;3.3. The Continuous Case;101
8.4;3.4. Computing Expectations by Conditioning;104
8.5;3.5. Computing Probabilities by Conditioning;113
8.6;3.6. Some Applications;120
8.7;Exercises;138
9;Chapter 4. Markov Chains;150
9.1;4.1. Introduction;150
9.2;4.2. Chapman-Kolmogorov Equations;153
9.3;4.3. Classification of States;156
9.4;4.4. Limiting Probabilities;164
9.5;4.5. Some Applications;174
9.6;4.6. Branching Processes;181
9.7;4.7. Time Reversible Markov Chains;184
9.8;4.8. Markov Decision Processes;195
9.9;Exercises;199
9.10;References;211
10;Chapter 5. The Exponential Distribution and the Poisson Process;212
10.1;5.1. Introduction;212
10.2;5.2. The Exponential Distribution;213
10.3;5.3. The Poisson Process;221
10.4;5.4. Generalizations of the Poisson Process;248
10.5;Exercises;256
10.6;References;267
11;Chapter 6. Continuous-Time Markov Chains;268
11.1;6.1. Introduction;268
11.2;6.2. Continuous-Time Markov Chains;269
11.3;6.3. Birth and Death Processes;271
11.4;6.4. The Kolmogorov Differential Equations;278
11.5;6.5. Limiting Probabilities;285
11.6;6.6. Time Reversibility;293
11.7;6.7. Uniformization;299
11.8;6.8. Computing the Transition Probabilities;302
11.9;Exercises;305
11.10;References;314
12;Chapter 7. Renewal Theory and Its Applications;316
12.1;7.1. Introduction;316
12.2;7.2. Distribution of N(t);318
12.3;7.3. Limit Theorems and Their Applications;322
12.4;7.4. Renewal Reward Processes;331
12.5;7.5. Regenerative Processes;338
12.6;7.6. Semi-Markov Processes;344
12.7;7.7. The Inspection Paradox;347
12.8;7.8. Computing the Renewal Function;349
12.9;Exercises;352
12.10;References;362
13;Chapter 8. Queueing Theory;364
13.1;8.1. Introduction;364
13.2;8.2. Preliminaries;365
13.3;8.3. Exponential Models;369
13.4;8.4. Network of Queues;385
13.5;8.5. The System M/G/1;394
13.6;8.6. Variations on the M/G/1;398
13.7;8.7. The Model G/M/1;403
13.8;8.8. Multiserver Queues;408
13.9;Exercises;414
13.10;References;423
14;Chapter 9. Reliability Theory;424
14.1;9.1. Introduction;424
14.2;9.2. Structure Functions;425
14.3;9.3. Reliability of Systems of Independent Components;431
14.4;9.4. Bounds on the Reliability Function;435
14.5;9.5. System Life as a Function of Component Lives;446
14.6;9.6. Expected System Lifetime;454
14.7;9.7. Systems with Repair;458
14.8;Exercises;462
14.9;References;469
15;Chapter 10. Brownian Motion and Stationary Processes;470
15.1;10.1. Brownian Motion;470
15.2;10.2. Hitting Times, Maximum Variable, and the Gambler's Ruin Problem;473
15.3;10.3. Variations on Brownian Motion;475
15.4;10.4. Pricing Stock Options;476
15.5;10.5. White Noise;487
15.6;10.6. Gaussian Processes;489
15.7;10.7. Stationary and Weakly Stationary Processes;492
15.8;10.8. Harmonic Analysis of Weakly Stationary Processes;497
15.9;Exercises;499
15.10;References;504
16;Chapter 11. Simulation;506
16.1;11.1. Introduction;506
16.2;11.2. General Techniques for Simulating Continuous Random Variables;511
16.3;11.3. Special Techniques for Simulating Continuous Random Variables;519
16.4;11.4. Simulating from Discrete Distributions;527
16.5;11.5. Stochastic Processes;534
16.6;11.6. Variance Reduction Techniques;545
16.7;11.7. Determining the Number of Runs;555
16.8;Exercises;555
16.9;References;564
17;Index;566