随机过程导论

　　本书是为那些有兴趣学习随机过程的概念、模型和计算方法的学生编写的，是随机过程课程的入门教材，适合管理、金融、工程、统计、计算机科学和应用数学等专业的高年级本科生或低年级研究生阅读。本书采用面向应用和计算的方式，强调通过各种示例和习题来开发学生在随机建模和分析中的实战能力，同时将计算的任务交给计算机去完成。

　　

　　随机过程是对随时间和空间变化的随机现象进行建模和分析的学科。许多年前，我们不能在现实问题求解中应用随机过程，但随着数值方法和计算工具的快速发展，这种状况已经发生了变化。本书很好地将计算机的使用和随机过程教学结合起来，采用MATLAB的计算机解题方法，使本书充满现代感，又具备实用的特点。本书采用面向应用和计算的方式，强调通过各种示例和习题来开发学生在随机建模和分析中的实战能力，同时将计算的任务交给计算机去完成。 本书是为那些有兴趣学习随机过程的概念、模型和计算方法的学生编写的，是随机过程课程的入门教材，适合管理、金融、工程、统计、计算机科学和应用数学等专业的高年级本科生或低年级研究生阅读

1 Introduction
1.0 Overview
1.1 Introduction
1.2 Discrete Random Variables and Generating Functions
1.3 Continuous Random Variables and Laplace Transforms
1.4 Some Mathematical Background
Problems
Bibliographic Notes
References
Appendix

2 Poisson Processes
2.0 Overview
2.1 Introduction
2.2 Properties of Poisson Processes
2.3 Nonhomogeneous Poisson Processes
2.4 Compound Poisson Processes
2.5 Filtered Poisson Processes
2.6 Two-Dimensional and Marked Poisson Processes
2.1 Poisson Arrivals See Time Averages (PASTA)
Problems
Bibliographic Notes
References
Appendix

3 Renewal Processes
3.0 Overview
3.1 Introduction
3.2 Renewal-Type Equations
3.3 Excess Life, Current Life, and Total Life
3.4 Renewal Reward Processes
3.5 Limiting Theorems, Stationary and Transient Renewal Processes
3.6 Regenerative Processes
3.7 Discrete Renewal Processes
Problems
Bibliographic Notes
References
Appendix

4 Discrete-Time Markov Chains
4.0 Overview
4.1 Introduction
4.2 Classification of States
4.3 Ergodic and Periodic Markov Chains
4.4 Absorbing Markov Chains
4.5 Markov Reward Processes
4.6 Reversible Discrete-Tune Markov Chains
Problems
Bibliographic Notes
References
Appendix

5 Continuous-Time Markov Chains
5.0 Overview
5.1 Introduction
5.2 The Kolmogorov Differential Equations
5.3 The Limiting Probabilities
5.4 Absorbing Continuous-Time Markov Chains
5.S Phase-Type Distributions
5.6 Uniformization
5.7 Continuous-Time Markov Reward Processes
5.8 Reversible Continuous-Time Markov Chains
Problems
Bibliographic Notes
References
Appendix

6 Markov Renewal and Semi-Regenerative Processes
6.0 Overview
6.1 Introduction
6.2 Markov Renewal Functions and Equations
6.3 Semi-Markov Processes and Related Reward Processes
6.4 Semi-Regenerative Processes
Problems
Bibliographic Notes
References
Appendix

7 Brownian Motion and Other Diffusion Processes
7.0 Overview
7.1 Introduction
7.2 Diffusion Processes
7.3 Ito's Calculus and Stochastic Differential Equations
7.4 Multidimensional Ito's Lemma
7.5 Control of Systems of Stochastic Differential Equations
Problems
Bibliographic Notes
References
Appendix
Appendix: Getting Started with MATLAB
Index