A Gentle Introduction to Stochastic Processes
"Stochastic Processes" is an advanced probability/statistics course. The content covers Markov chains, Brownian motion, stochastic differential equations, and diffusion processes, providing in-depth explanations of knowledge such as system state transitions and the laws of random motion. It also involves cutting-edge topics such as stochastic partial differential equations and stochastic categories. The course uses computer languages such as Python and MATLAB to implement algorithms, simulate state transitions, and solve numerical solutions of equations, helping students combine theory with practice and cultivate the ability to use stochastic processes to solve complex problems, laying a solid foundation for the study and research in fields such as natural sciences, engineering, and finance.
讲师
日期
2025年03月17日 至 06月11日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周一,周三 | 13:30 - 15:05 | A7-307 | ZOOM 07 | 559 700 6085 | BIMSA |
网站
修课要求
Measure Theory, Probability Theory/Statistics, Linear Algebra, Real Analysis/Functional Analysis
课程大纲
| Date | Content | Remarks |
| ---- | ---- | ---- |
| Week 1, Session 1 | Review of probability theory/statistics | Principles |
| Week 1, Session 2 | Measure theory | Principles |
| Week 2, Session 1 | Basics of stochastic processes 1 | - |
| Week 2, Session 2 | Basics of stochastic processes 2 | - |
| Week 3, Session 1 | Basics of stochastic processes 3 | - |
| Week 3, Session 2 | Basics of stochastic processes 4 | Paper interpretation |
| Week 4, Session 1 | Martingale theory 1 | - |
| Week 4, Session 2 | Martingale theory 2 | Paper interpretation |
| Week 5, Session 1 | Markov chains 1 | Principles |
| Week 5, Session 2 | Markov chains 2 | Principles |
| Week 6, Session 1 | Markov chain Monte Carlo | Paper interpretation |
| Week 6, Session 2 | Applications of Markov chains | - |
| Week 7, Session 1 | Temporal processes 1 | Paper interpretation |
| Week 7, Session 2 | Temporal processes 2 | Paper interpretation |
| Week 8, Session 1 | Stochastic differential equations 1 | Presentation of works |
| Week 8, Session 2 | Stochastic differential equations 2 | Presentation of works |
| Week 9, Session 1 | Numerical SDE 1 | Principles, paper interpretation |
| Week 9, Session 2 | Numerical SDE 2 | Paper interpretation |
| Week 10, Session 1 | Stochastic PDE 1 | - |
| Week 10, Session 2 | Stochastic PDE 2 | - |
| Week 11, Session 1 | Stochastic optimization 1 | - |
| Week 11, Session 2 | Stochastic optimization 2 | Presentation of works |
| Week 12, Session 1 | Applications of machine learning 1 | - |
| Week 12, Session 2 | Applications of machine learning 2 | - |
| ---- | ---- | ---- |
| Week 1, Session 1 | Review of probability theory/statistics | Principles |
| Week 1, Session 2 | Measure theory | Principles |
| Week 2, Session 1 | Basics of stochastic processes 1 | - |
| Week 2, Session 2 | Basics of stochastic processes 2 | - |
| Week 3, Session 1 | Basics of stochastic processes 3 | - |
| Week 3, Session 2 | Basics of stochastic processes 4 | Paper interpretation |
| Week 4, Session 1 | Martingale theory 1 | - |
| Week 4, Session 2 | Martingale theory 2 | Paper interpretation |
| Week 5, Session 1 | Markov chains 1 | Principles |
| Week 5, Session 2 | Markov chains 2 | Principles |
| Week 6, Session 1 | Markov chain Monte Carlo | Paper interpretation |
| Week 6, Session 2 | Applications of Markov chains | - |
| Week 7, Session 1 | Temporal processes 1 | Paper interpretation |
| Week 7, Session 2 | Temporal processes 2 | Paper interpretation |
| Week 8, Session 1 | Stochastic differential equations 1 | Presentation of works |
| Week 8, Session 2 | Stochastic differential equations 2 | Presentation of works |
| Week 9, Session 1 | Numerical SDE 1 | Principles, paper interpretation |
| Week 9, Session 2 | Numerical SDE 2 | Paper interpretation |
| Week 10, Session 1 | Stochastic PDE 1 | - |
| Week 10, Session 2 | Stochastic PDE 2 | - |
| Week 11, Session 1 | Stochastic optimization 1 | - |
| Week 11, Session 2 | Stochastic optimization 2 | Presentation of works |
| Week 12, Session 1 | Applications of machine learning 1 | - |
| Week 12, Session 2 | Applications of machine learning 2 | - |
参考资料
1. R. F. Boss. Stochastic processes, 1998
2. Christian P. Robert, George Casella. Monte Carlo Statistical Methods, New York: Springer-Verlag, 1999.
3. I. Karatzas, S. E. Shreve. Brownian Motion and Stochastic Calculus, Springer, 2000.
4. L. Aggoun, R. Elliott. Measure Theory and Filtering Introduction with Applications, Cambridge University Press, 2004
2. Christian P. Robert, George Casella. Monte Carlo Statistical Methods, New York: Springer-Verlag, 1999.
3. I. Karatzas, S. E. Shreve. Brownian Motion and Stochastic Calculus, Springer, 2000.
4. L. Aggoun, R. Elliott. Measure Theory and Filtering Introduction with Applications, Cambridge University Press, 2004
听众
Advanced Undergraduate
, Graduate
, 博士后
, Researcher
视频公开
公开
笔记公开
公开
语言
中文
, 英文
讲师介绍
宋丛威于2011年在浙江大学理学院取得应用数学硕士学位，于2014年在浙江大学数学系取得基础数学博士学位，2014-2021年在浙江工业大学之江学院任讲师，2021至今任BIMSA助理研究员。主要研究方向：小波分析，调和分析，机器学习。