應用隨機過程概率模型導論（英文版·第9版）

1.Introduction to Probability Theory
1.1.Introduction
1.2.Sample Space and Events
1.3.Probabilities Defined on Events
1.4.Conditional Probabilities
1.5.Independent Events
1.6.Bayes' Formula
Exercises
References
2.Random Variables
2.1.Random Variables
2.2.Discrete Random Variables
2.3.Continuous Random Variables
2.4.Expectation of a Random Variable
2.5.Jointly Distributed Random Variables
2.6.Moment Generating Functions
2.7.Limit Theorems
2.8.Stochastic Processes
Exercises
References
3.Conditional Probability and Conditional Expectation
3.1.Introduction
3.2.The Discrete Case
3.3.The Continuous Case
3.4.Computing Expectations by Conditioning
3.5.Computing Probabilities by Conditioning
3.6.Some Applications
3.7.An Identity for Compound Random Variables
Exercises
4.Markov Chains
4.1.Introduction
4.2.Chapman-Kolmogorov Equations
4.3.Classification of States
4.4.Limiting Probabilities
4.5.Some Applications
4.6.Mean Time Spent in Transient States
4.7.Branching Processes
4.8.Time Reversible Markov Chains
4.9.Markov Chain Monte Carlo Methods
4.10.Markov Decision Processes
4.11.Hidden Markov Chains
Exercises
References
5.The Exponential Distribution and the Poisson Process
5.1.Introduction
5.2.The Exponential Distribution
5.3.The Poisson Process
5.4.Generalizations of the Poisson Process
Exercises
References
6.Continuous-Time Markov Chains
7.Renewal Theory and Its Applications
8.Queueing Theory
9.Reliability Theory
10.Brownian Motion and Stationary Processes
11.Simulation
Appendix: Solutions to Starred Exercises
Index