| 词条 | 应用随机过程概率模型导论 |
| 释义 | § 【内容介绍】 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】 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 【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。 |
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