2024 Faculty Courses School of Computing Department of Mathematical and Computing Science Graduate major in Mathematical and Computing Science
Applied Probability
- Academic unit or major
- Graduate major in Mathematical and Computing Science
- Instructor(s)
- Naoto Miyoshi / Yumiharu Nakano
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 7-8 Mon / 7-8 Thu
- Class
- -
- Course Code
- MCS.T410
- Number of credits
- 200
- Course offered
- 2024
- Offered quarter
- 3Q
- Syllabus updated
- Mar 14, 2025
- Language
- English
Syllabus
Course overview and goals
This course focuses on stochastic processes and its applications. In this year, topics include the theory of point processes and its application to modeling and analysis of wireless networks.
Course description and aims
At the end of this course, students will be able to understand the fundamental theory of point processes, one of the basic stochastic processes, and its application to modeling and analysis of wireless communication networks.
Keywords
Point processes, Poisson processes, Cox processes, stationary point processes, Palm theory, wireless networks.
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
The document of each lecture will be uploaded to T2SCHOLA.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Preliminaries: Measures and Integrals | Define measures, integrals and probability, and study their fundamental notions |
| Class 2 | Random measures, point processes and their distributions | Define random measures and point processes, and characterize their distributions |
| Class 3 | Poisson point processes | Define the Poisson point processes |
| Class 4 | Poisson point processes (continued) | Reveal some properties of Poisson point processes |
| Class 5 | Operations on point processes | Study some operations on point processes |
| Class 6 | Cox point processes and cluster point processes | Define Cox point processes and cluster point processes, and reveal their properties |
| Class 7 | Determinantal point processes | Define determinantal point processes and reveal their properties |
| Class 8 | Palm distributions | Define Palm distributions |
| Class 9 | Higher order Palm distributions | Introduce higher order Palm distributions and reveal their properties |
| Class 10 | Stationary random measures and stationary point processes | Reveal some properties of stationary random measures and point processes |
| Class 11 | Palm calculus for stationary random measures and point processes | Study the Palm calculus for stationary random measures and point processes |
| Class 12 | Basic formulas in Palm calculus and their applications | Show some basic properties of stationary point processes using the Palm calculus |
| Class 13 | Application to wireless networks | Introduce a spatial point process model of cellular wireless networks |
| Class 14 | Application to wireless networks (continued) | Derive the coverage probability for cellular network models using various point processes |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None.
Reference books, course materials, etc.
[1] F. Baccelli, B. Blaszczyszyn and Mohamed Karray. Random Measures, Point Processes, and Stochastic Geometry. HAL-02460214 (2020)
[2] G. Last and M. Penrose. Lectures on the Poisson Process. Cambridge University Press, 2017.
Evaluation methods and criteria
Report assignment(s).
Related courses
- MCS.T212 ： Fundamentals of Probability
- MCS.T312 ： Markov Analysis
- MCS.T304 ： Lebesgue Interation
Prerequisites
Understanding of the related courses above (you do not have to take these courses if you understand the contents of them).