# SM4202 Random Processes

Dear students, I welcome feedback from you: Link

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

### 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* 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

- Ross, S. (2009). A First Course in Probability.
- Ross, S. M. (2014). Introduction to probability models. Academic Press.
- Grimmet, G. & Stirzaker, D. (2020). Probability and Random Processes. Oxford University Press.
- Norris, J. R. (1998). Markov Chains. Cambridge University Press.