随机过程在数学、科学和工程中有着越来越广泛的应用。本书包括随机过程一些基本而又重要的内容:条件期望,Markov链,Poisson过程和Brown运动;同时也包括Ito积分和随机微分方程等应用范围越来越广的内容。本书的习题是其基本内容的延伸,而且有十分完整的解答,非常适合高年级本科生和研究生自学使用或用作教学参考书。

1. Review of Probability
1.1 Events and Probability
1.2 Random Variables
1.3 Conditional Probability and Independence
1.4 Solutions
2. Conditional Expectation
2.1 Conditioning on an Event
2.2 Conditioning on a Discrete Random Variable
2.3 Conditioning on an Arbitrary Random Variable
2.4 Conditioning on a a-Field
2.5 General Properties
2.5 Various Exercises on Conditional Expectation
2.7 Solutions
3 Martingales in Discrete Time
3.1 SequencesofRandomVariables
3.2 Filtrations
3.3 Martingales
3.4 Games or Uhance
3.5 StoppingTimes
3.5 Optional Stopping Theorem
3.7 Solutions
4 Martingale Inequalities and Convergence
4.1 Doob's Martingale Inequalities
……
5. Markov Chains
6. Stochastic Processes in Continuous Time
7. It5 Stochastic Calculus
Index