CST 3526: Stochastic Process

“Education is not the filling of a pail, but the lighting of a fire.”

Description

Time: Thu 6:30PM – 8:55PM

Location: Building A, Room 214

Office hours: By appointment

Teaching Assistant: Wenjie Wang (wenjie_wang[AT]tongji[DOT]edu[DOT]cn)

This course is designed for undergraduate students majoring in Computer Science and Data Science, and is jointly taught by Prof. Ziqiao Wang (Week 1-2, Week 11-16) and Prof. Mingliang Xiong (Week 3-10). The course provides an introduction to the fundamental concepts and methods of stochastic processes, with an emphasis on their applications in real-world problems. Through a balanced integration of theory and practice, students will develop a systematic understanding of stochastic processes and establish a solid foundation for advanced courses in their major.

This course will cover the following topics: 1) Review of Basic Probability Theory (axioms of probability, conditional probability, independence, random variables, CDF, PMF, PDF, function of random variables, multiple random variables, expectation and variance, etc) by Prof. Wang; 2) Classifications and Numerical Characteristics of Stochastic Processes by Prof. Xiong; 3) Markov Processes (C–K equations, Markov chains, limit behavior and stationary distributions, recurrence and transience analysis, continuous-time parameter Markov processes with discrete state space, limit properties of purely discontinuous Markov chains, birth–death processes, etc) by Prof. Xiong; 3) Poisson Processes (relationship between Poisson process and exponential distribution, residual lifetime and age properties, conditional distribution of arrival times, non-homogeneous Poisson processes, compound Poisson processes, conditional Poisson processes, renewal processes, filtered Poisson processes, etc) by Prof. Xiong; 4) Second-order Processes (wide-sense stationary processes, orthogonal increment processes, mean-square calculus and ergodic theory, etc) by Prof. Wang; 5) Gaussian processes (multivariate Gaussian distribution and its properties, Gauss–Markov property, behavior of Gaussian processes under nonlinear systems, narrowband Gaussian processes and Brownian motion, etc) by Prof. Wang.

Announcement

• First lecture starts on September 18th.

Reference textbooks

• 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

Grading

participation(10%), in-class performance(10%), two assignments(each 15%), and a final project (50%).

Schedule of Classes (Tentative)

• Week 1 (Sep. 18): Review of Probability Theory I (Prof. Wang) [Lecture Note]

• Week 2 (Sep. 25): Review of Probability Theory II (Prof. Wang) [Lecture Note]

• Week 3 (Oct 2): National Day Break

• Week 4 (Oct 9): Classifications and Numerical Characteristics of Stochastic Processes (Prof. Xiong) [Lecture Note]

• Week 5 (Oct 16): Markov Processes I (Prof. Xiong)

• Week 6 (Oct 23): Markov Processes II (Prof. Xiong)

• Week 7 (Oct 30): Markov Processes III (Prof. Xiong)

• Week 8 (Nov 6): Poisson Processes I (Prof. Xiong)

• Week 9 (Nov 13): Poisson Processes II (Prof. Xiong)

• Week 10 (Nov 20): Poisson Processes III (Prof. Xiong)

• Week 11 (Nov. 27): Second-order Processes I (Prof. Wang)

• Week 12 (Dec. 4): Second-order Processes II (Prof. Wang)

• Week 13 (Dec. 11): Gaussian Processes I (Prof. Wang)

• Week 14 (Dec. 18): Gaussian Processes II (Prof. Wang)

• Week 15 (Dec. 25): Advanced Topic: TBD (Prof. Wang)

• Week 16 (TBD): Advanced Topic:TBD (Prof. Wang)