2021 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
- 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
- 2021
- Offered quarter
- 3Q
- Syllabus updated
- Jul 10, 2025
- Language
- Japanese
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, coverage probability.
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
On-line lectures. 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 | Operations on point processes |
Study some operations on point processes |
| Class 5 | Cox point processes |
Define Cox point processes and reveal their properties |
| Class 6 | Determinantal point processes |
Define determinantal point processes and reveal their properties |
| Class 7 | Palm probability |
Define Palm probability |
| Class 8 | Stationary point processes |
Reveal some properties of stationary point processes |
| Class 9 | Palm theory for stationary point processes |
Study the Palm theory for stationary point processes |
| Class 10 | Basic properties of stationary point processes |
Show some basic properties of stationary point processes using the Palm calculus |
| Class 11 | Application to cellular networks |
Introduce a spatial point process model of cellular wireless networks |
| Class 12 | Coverage probability of cellular network models |
Derive the coverage probability for cellular network models using various point processes |
| Class 13 | Application to wireless broadcasting |
Introduce a spatial point process model of wireless broadcasting |
| Class 14 | TBA |
TBA |
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).