### 2021　Applied Probability

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Graduate major in Mathematical and Computing Science
Instructor(s)
Miyoshi Naoto  Nakano Yumiharu
Class Format
Lecture
Media-enhanced courses
Day/Period(Room No.)
Mon7-8()  Thr7-8()
Group
-
Course number
MCS.T410
Credits
2
2021
Offered quarter
3Q
Syllabus updated
2021/9/30
Lecture notes updated
-
Language used
Japanese
Access Index

### Course description and aims

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.

### Student learning outcomes

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 that will be developed

 ✔ 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/Required learning

Course schedule Required learning
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

### Out-of-Class Study Time (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.

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.

### Assessment criteria and methods

Report assignment(s).

### Related courses

• MCS.T212 ： Fundamentals of Probability
• MCS.T312 ： Markov Analysis
• MCS.T304 ： Lebesgue Interation

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

Understanding of the related courses above (you do not have to take these courses if you understand the contents of them).