2025 (Current Year) 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 (W8E-306(W832)) / 7-8 Thu (W8E-306(W832))
Class: -
Course Code: MCS.T410
Number of credits: 200
Course offered: 2025
Offered quarter: 3Q
Syllabus updated: Sep 26, 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.

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 LMS.

Course schedule/Objectives

	Course schedule	Objectives
Class 1	Preliminaries: Measures and Integrals	Define measures, integrals and probability, and learn 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, and learn some of their properties
Class 4	Operations on point processes	Learn some operations on point processes
Class 5	Cox point processes and cluster point processes	Define Cox point processes and cluster point processes, and learn their properties
Class 6	Determinantal point processes	Define determinantal point processes and learn their fundamental properties
Class 7	Palm distributions	Define Palm distributions, and learn their fundamental properties
Class 8	Higher order Palm distributions	Introduce higher order Palm distributions and learn their properties
Class 9	Stationary random measures and point processes	Learn some properties of stationary random measures and point processes
Class 10	Palm calculus for stationary random measures and point processes	Learn the Palm calculus for stationary random measures and point processes
Class 11	Basic formulas in Palm calculus and their applications	Learn how to use Palm calculus to show the basic properties of stationary point processes
Class 12	Applications to wireless networks	Introduce a spatial point process model of cellular wireless networks
Class 13	Application to wireless networks (continued)	Derive the coverage probability for cellular network models using various point processes
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).