随机过程基础
课程编号：S131GA04
随机过程基础
Stochastic Processes
学时：32 学分：2 开课时间：秋 季
授课单位：理学院 任课教师：王家生
一、课程内容简介
本课程分为4章。
1．概率论基础：条件数学期望，特征函数，n 维正态分布。
2．随机过程的基本概念：有限维分布函数族，随机过程的数字特征。正态过程，独立增量过程，维纳过程，泊松过程 ，更新过程。
3. 马尔可夫链：离散时间的马尔可夫链，状态的分类，遍历性，平稳分布。连续时间的马尔可夫链，生灭过程。
4．平稳过程：协方差函数的谱分解，平稳过程的谱分解，线性时不变系统，遍历定理，采样定理。
通过本课程学习，研究生能基本掌握随机过程的基本概念、基本理论与方法，并为完成毕业论文做好准备。
There are four chapters in stochastic processes.
1. basis of probability theory: conditional mathematical expectation, characteristic function, n-dimensional normal distribution.
2. basic concepts of stochastic processes: family of finite dimensional distribution functions, numerical characteristics of stochastic processes. normal process, process with independent increaments,Wiener process, Poisson process, renewal process.
3. Markov chain: discret-time Markov chains, classification of states, ergodic, stationary distribution. Continuous-time Markov chains, birth and death process.
4. stationary process: spectral decomposition of covariance function, spectral decomposition of stationary process, linear time invariant system, ergodic theorem, sampling theorem.
Students should muster the basic concept ,theory and methods of stochastic processes through studying this course. It is helpful for improving the students’ ability and it is beneficial for the their mathematic career.
二、先修课程
概率论、线性代数
三、教材
随机过程基础，王家生、刘嘉焜，天津大学出版社，2003
四、主要参考书目及文献
1、应用随机过程，刘嘉焜，科学出版社，2004
2、S . M .Ross. Stochastic Process. John Wiley & Sons，1983