应用随机过程概率模型导论
【内容介绍】
本书是国际知名统计学家Sheldon M．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。
【本书目录】
1Introduction to Probability Theory1
1.1Introduction1
1.2Sample Space and Events1
1.3Probabilities Defined on Events4
1.4Conditional Probabilities7
1.5Independent Events10
1.6Bayes' Formula12
Exercises15
References21
2Random Variables23
2.1Random Variables23
2.2Discrete Random Variables27
2.3Continuous Random Variables34
2.4Expectation of a Random Variable38
2.5Jointly Distributed Random Variables43
2.6Moment Generating Functions64
2.7Limit Theorems77
2.8Stochastic Processes83
Exercises85
References96
3Conditional Probability and Conditional Expectation97
3.1Introduction97
3.2The Discrete Case97
3.3The Continuous Case102
3.4Computing Expectations by Conditioning105
3.5Computing Probabilities by Conditioning119
3.6Some Applications Exercises136
Exercises161
4Markov Chains181
4.1Introduction181
4.2Chapman-Kolmogorov Equations185
4.3Classification of States189
4.4Limiting Probabilities200
4.5Some Applications213
4.6Mean Time Spent in Transient States226
4.7Branching Processes228
4.8Time Reversible Markov Chains232
4.9Markov Chain Monte Carlo Methods243
4.10Markov Decision Processes248
Exercises252
References268
5The Exponential Distribution and the Poisson Process269
5.1Introduction269
5.2The Exponential Distribution270
5.3The Poisson Process288
5.4Generalizations of the Poisson Process316
Exercises330
References348
6Continuous-Time Markov Chains349
6.1Introduction349
6.2Continuous-Time Markov Chains350
6.3Birth and Death Processes352
6.4The Transition Probability Function Pij (t)359
6.5Limiting Probabilities368
6.6Time Reversibility376
6.7Uniformization384
6.8Computing the Transition Probabilities388
Exercises390
References399
7Renewal Theory and Its Applications401
7.1Introduction401
7.2Distribution of N(t)403
7.3Limit Theorems and Their Applications407
7.4Renewal Reward Processes416
7.5Regenerative Processes425
7.6Semi-Markov Processes434
7.7The Inspection Paradox437
7.8Computing the Renewal Function440
7.9Applications to Patterns443
7.10The Insurance Ruin Problem455
Exercises460
References472
8Queueing Theory475
8.1Introduction475
8.2Preliminaries476
8.3Exponential Models480
8.4Network of Queues496
8.5The System M/G/1507
8.6Variations on the M/G/1510
8.7The Model G/M/1519
8.8A Finite Source Model525
8.9Multiserver Queues528
Exercises534
References546
9Reliability Theory547
9.1Introduction547
9.2Structure Functions547
9.3Reliability of Systems of Independent Components554
9.4Bounds on the Reliability Function559
9.5System Life as a Function of Component Lives571
9.6Expected System Lifetime580
9.7Systems with Repair586
Exercises593
References600
10Brownian Motion and Stationary Processes601
10.1Brownian Motion601
10.2Hitting Times, Maximum Variable, and the Gambler's Ruin Problem605
10.3Variations on Brownian Motion607
10.4Pricing Stock Options608
10.5White Noise620
10.6Gaussian Processes622
10.7Stationary andWeakly Stationary Processes625
10.8Harmonic Analysis of Weakly Stationary Processes630
Exercises633
References638
11Simulation639
11.1Introduction639
11.2General Techniques for Simulating Continuous Random Variables644
11.3Special Techniques for Simulating Continuous Random Variables653
11.4Simulating from Discrete Distributions661
11.5Stochastic Processes668
11.6Variance Reduction Techniques679
11.7Determining the Number of Runs696
11.8Coupling from the Past696
Exercises699
References707
Appendix: Solutions to Starred Exercises709
Index749
【作者介绍】
国际知名统计学家，加州大学伯克利分校工业工程与运筹系教授。毕业于斯坦福大学统计系。研究领域包括：随机模型、仿真模拟、统计分析、金融数学等。罗斯教授是多本畅销数学和统计教材的作者。