“Education is not the filling of a pail, but the lighting of a fire.”
Instructor: Ziqiao Wang
Time: Thu 6:30PM – 8:55PM
Location: Building B, Room 402
Office hours: By appointment
Teaching Assistant: Xingyu Guo (2634346[AT]tongji[DOT]edu[DOT]cn)
This course is designed for third-year undergraduate students majoring in Computer Science. It introduces the fundamental concepts and methods of stochastic processes, with an emphasis on modeling random systems and understanding their evolution. Through conceptual explanations, mathematical analysis, and numerical examples, students will develop a systematic understanding of stochastic processes and a foundation for further study.
The course will cover the following topics:
Review of Basic Probability Theory: probability axioms, conditional probability and independence, random variables and distributions, expectation and variance, covariance, conditional expectation, and basic limit theorems.
Classifications and Numerical Characteristics of Stochastic Processes: index sets, state spaces, sample paths, finite-dimensional distributions, mean and covariance functions, and basic process classifications.
Markov Processes: Markov chains, transition probabilities, Chapman–Kolmogorov equations, state classification, recurrence and transience, stationary distributions, limiting behavior, and basic hitting-time problems.
Second-order Processes: autocorrelation and autocovariance, wide-sense stationarity, mean-square convergence and continuity, basic mean-square calculus, and linear prediction.
Poisson Processes: counting processes, exponential waiting times, arrival-time distributions, superposition and thinning, non-homogeneous Poisson processes, renewal processes, and an introduction to continuous-time Markov models and birth–death processes.
Gaussian Processes: multivariate Gaussian distributions, Gaussian conditioning, covariance kernels, and Brownian motion.
Advanced topic.
The first lecture starts on Thursday, September 17, 2026 (Week 1).
National Day break: October 1–7. There is no class on Thursday, October 1 (Week 3).
随机过程及其应用，陆大䋮、张颢 编著
Probability, Statistics, and Random Processes for Electrical Engineering, by Alberto Leon-Garcia (this book is available online)
Stochastic Processes, by Sheldon M. Ross
随机过程, Sheldon M. Ross 著，龚光鲁 译
随机过程讲义， 孙应飞 著 (the corresponding course video can be found at Bilibili)
Stochastic Processes: Theory for Applications, by Robert G. Gallager
随机过程，张颢老师，中国科学院大学课程视频：Bilibili.
Participation: 10%.
In-class quizzes: 40%. Five quizzes are tentatively planned. The lowest quiz score will be dropped, and the best four scores will be averaged.
Final project: 50%. Details will be announced later.
Week numbers count calendar weeks, including the National Day break. There are 15 class meetings over 16 weeks. The schedule and quiz dates are tentative and subject to university holiday and make-up class arrangements.
Week 1 (Sep. 17): Review of Probability Theory I [Lecture Note]
Week 2 (Sep. 24): Review of Probability Theory II [Lecture Note]
Week 3 (Oct. 1): National Day Break (no class)
Week 4 (Oct. 8): Review of Probability Theory III [Lecture Note]
Week 5 (Oct. 15): Classifications and Numerical Characteristics of Stochastic Processes [Quiz 1] [Lecture Note]
Week 6 (Oct. 22): Markov Processes I
Week 7 (Oct. 29): Markov Processes II
Week 8 (Nov. 5): Second-order Processes I [Quiz 2]
Week 9 (Nov. 12): Second-order Processes II
Week 10 (Nov. 19): Poisson Processes I (by Guest Lecturer Prof. Lu Liu) [Quiz 3]
Week 11 (Nov. 26): Poisson Processes II (by Guest Lecturer Prof. Lu Liu)
Week 12 (Dec. 3): Poisson Processes III (by Guest Lecturer Prof. Lu Liu)
Week 13 (Dec. 10): Poisson Processes IV: Continuous-Time Markov Models (by Guest Lecturer Prof. Lu Liu)
Week 14 (Dec. 17): Gaussian Processes I [Quiz 4]
Week 15 (Dec. 24): Gaussian Processes II: Brownian Motion
Week 16 (Dec. 31): Advanced topic [Quiz 5]
Quizzes are closed-book and completed independently, without electronic devices or generative AI unless explicitly authorized. For projects, AI may assist brainstorming, debugging, or editing, but students must disclose the tool and its use, verify references and outputs, and independently explain all core submitted work. Fabricated data, experiments, references, or undisclosed substitution for the student's own analysis are not permitted.