SM4202 Random Processes

I will be teaching SM4202 for the first half of the semester (roughly 7 weeks) for the August 2020 semester.

Syllabus

Here are the topics I intend to cover for this course. This may change depending on how we get on with the course.

  • Chapter 1: Probability recap

    • Recall fundamental concepts in mathematical probability
    • Recap of discrete and continuous distributions
    • Properties of means and variances
    • Generating functions

  • Chapter 2: Discrete time stochastic processes

    • Definitions and examples
    • Discrete Markov chains
    • Transition probabilities, stationary transition probabilities, $n$-step transition matrices
    • Chapman-Kolmogorov equations
    • State diagrams and classification of states
    • Periodicity, recurrence and transience

  • Chapter 3: Continuous time stochastic processes

    • Basic concepts and definitions
    • Instantaneous transition rates
    • $Q$ matrices (generator matrices)
    • Kolmogorov equations
    • Invariant measures for irreducible, continuous Markov processes

Schedule

  • W4 Tue 18/8/2020 1330-1530 @ 1A.62; Lecture (Chapter 1)
  • W4 Wed 19/8/2020 1330-1530 @ 1A.62; Lecture (Chapter 1)
  • W5 Tue 25/8/2020 1300-1530 @ 1A.62; Lecture (Chapter 2)
  • W5 Wed 26/8/2020 1230-1400 @ 1A.62; Lecture (Chapter 2)
  • W5 Sat 29/8/2020 0800-1000 @ 1A.62; Tutorial (Exercise 1)
  • W6 Tue 01/9/2020 1330-1530 @ 1A.62; Lecture (Chapter 2)
  • W6 Wed 02/9/2020 1330-1530 @ 1A.62; Lecture (Chapter 2)
  • W6 Sat 05/9/2020 0800-1000 @ 1A.62; Tutorial (Exercise 2)
  • W7 Tue 08/9/2020 1330-1530 @ 1A.62; Lecture (Chapter 3)
  • W7 Wed 09/9/2020 1330-1530 @ 1A.62; Lecture (Chapter 3)
  • MIDSEM Mon 14/9/2020 0800-1100 @ 1A.62; Lecture and Tutorial (Chapter 3 & Exercise 3)
CLASS TEST is scheduled for Sat 26/9/2020 @ 0830-0930. Covers Chapters 1 and 2 only.

Lecture Notes

Download lecture notes from my shared Google Drive.

Exercise Sheets

Statistical Tables

Supplementary Reading

Last updated on 3 Apr 2024