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.
Lecturer
Date
17th March ~ 11th June, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday,Wednesday | 13:30 - 15:05 | A7-307 | ZOOM 07 | 559 700 6085 | BIMSA |
Website
Prerequisite
Measure Theory, Probability Theory/Statistics, Linear Algebra, Real Analysis/Functional Analysis
Syllabus
| 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 | - |
Reference
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
Audience
Advanced Undergraduate
, Graduate
, Postdoc
, Researcher
Video Public
Yes
Notes Public
Yes
Language
Chinese
, English
Lecturer Intro
Congwei Song received the master degree in applied mathematics from the Institute of Science in Zhejiang University of Technology, and the Ph.D. degree in basic mathematics from the Department of Mathematics, Zhejiang University, worked in Zhijiang College of Zhejiang University of Technology as an assistant from 2014 to 2021, from 2021 on, worked in BIMSA as asistant researcher. His research interests include machine learning, as well as wavelet analysis and harmonic analysis.