应用随机过程 概率模型导论 第8版
作者：（美）罗斯 著
出版时间：2006年版
内容简介
本书实例丰富，涉及多学科各种概率模型。主要内容有随机变量、条件概率及条件期望、离散及连续马尔科夫链、指数分布、泊松过程、布朗运动及平稳过程、更新理论及排队论等，最后介绍了随机模拟。本书写得极其生动和直观，并附有大量的不同领域的习题和实用的例子。.本书可作为概率论与统计，计算机科学、保险学、物理学和社会科学、生命科学、管理科学与工程学专业随机过程基础课教材。本书是国际知名统计学家SheldonM．Ross所著的关于基础概率理论和随机过程的经典教材，被加州大学伯克利分校、哥伦比亚大学、普度大学、密歇根大学、俄勒冈州立大学、华盛顿大学等众多国外知名大学所采用。..与其他随机过程教材相比，本书非常强调实践性，内含极其丰富的例子和习题，涵盖了众多学科的各种应用；作者富于启发而又不失严密性的叙述方式，有助于读者建立概率思维方式，培养对概率理论、随机过程的直观感觉。对那些需要将概率理论应用于精算学、运筹学、物理学、工程学、计算机科学、管理学和社会科学的读者，本书是一本极好的教材或参考书。
目 录
1 Introduction to Probability Theory 1
1.1 Introduction 1
1.2 Sample Space and Events 1
1.3 Probabilities Defined on Events 4
1.4 Conditional Probabilities 7
1.5 Independent Events 10
1.6 Bayes' Formula 12
Exercises 15
References 21
2 Random Variables 23
2.1 Random Variables 23
2.2 Discrete Random Variables 27
2.3 Continuous Random Variables 34
2.4 Expectation of a Random Variable 38
2.5 Jointly Distributed Random Variables 43
2.6 Moment Generating Functions 64
2.7 Limit Theorems 77
2.8 Stochastic Processes 83
Exercises 85
References 96
3 Conditional Probability and Conditional Expectation 97
3.1 Introduction 97
3.2 The Discrete Case 97
3.3 The Continuous Case 102
3.4 Computing Expectations by Conditioning 105
3.5 Computing Probabilities by Conditioning 119
3.6 Some Applications Exercises 136
Exercises 161
4 Markov Chains 181
4.1 Introduction 181
4.2 Chapman-Kolmogorov Equations 185
4.3 Classification of States 189
4.4 Limiting Probabilities 200
4.5 Some Applications 213
4.6 Mean Time Spent in Transient States 226
4.7 Branching Processes 228
4.8 Time Reversible Markov Chains 232
4.9 Markov Chain Monte Carlo Methods 243
4.10 Markov Decision Processes 248
Exercises 252
References 268
5 The Exponential Distribution and the Poisson Process 269
5.1 Introduction 269
5.2 The Exponential Distribution 270
5.3 The Poisson Process 288
5.4 Generalizations of the Poisson Process 316
Exercises 330
References 348
6 Continuous-Time Markov Chains 349
6.1 Introduction 349
6.2 Continuous-Time Markov Chains 350
6.3 Birth and Death Processes 352
6.4 The Transition Probability Function Pij (t) 359
6.5 Limiting Probabilities 368
6.6 Time Reversibility 376
6.7 Uniformization 384
6.8 Computing the Transition Probabilities 388
Exercises 390
References 399
7 Renewal Theory and Its Applications 401
7.1 Introduction 401
7.2 Distribution of N(t) 403
7.3 Limit Theorems and Their Applications 407
7.4 Renewal Reward Processes 416
7.5 Regenerative Processes 425
7.6 Semi-Markov Processes 434
7.7 The Inspection Paradox 437
7.8 Computing the Renewal Function 440
7.9 Applications to Patterns 443
7.10 The Insurance Ruin Problem 455
Exercises 460
References 472
8 Queueing Theory 475
8.1 Introduction 475
8.2 Preliminaries 476
8.3 Exponential Models 480
8.4 Network of Queues 496
8.5 The System M/G/1 507
8.6 Variations on the M/G/1 510
8.7 The Model G/M/1 519
8.8 A Finite Source Model 525
8.9 Multiserver Queues 528
Exercises 534
References 546
9 Reliability Theory 547
9.1 Introduction 547
9.2 Structure Functions 547
9.3 Reliability of Systems of Independent Components 554
9.4 Bounds on the Reliability Function 559
9.5 System Life as a Function of Component Lives 571
9.6 Expected System Lifetime 580
9.7 Systems with Repair 586
Exercises 593
References 600
10 Brownian Motion and Stationary Processes 601
10.1 Brownian Motion 601
10.2 Hitting Times, Maximum Variable, and the Gambler's Ruin Problem 605
10.3 Variations on Brownian Motion 607
10.4 Pricing Stock Options 608
10.5 White Noise 620
10.6 Gaussian Processes 622
10.7 Stationary andWeakly Stationary Processes 625
10.8 Harmonic Analysis of Weakly Stationary Processes 630
Exercises 633
References 638
11 Simulation 639
11.1 Introduction 639
11.2 General Techniques for Simulating Continuous Random Variables 644
11.3 Special Techniques for Simulating Continuous Random Variables 653
11.4 Simulating from Discrete Distributions 661
11.5 Stochastic Processes 668
11.6 Variance Reduction Techniques 679
11.7 Determining the Number of Runs 696
11.8 Coupling from the Past 696
Exercises 699
References 707
Appendix: Solutions to Starred Exercises 709
Index 749
