2022 Applied Probability

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Academic unit or major
Graduate major in Mathematical and Computing Science
Miyoshi Naoto  Nakano Yumiharu 
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Mon7-8(W832)  Thr7-8(W832)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
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.


Point processes, Poisson processes, Cox processes, stationary point processes, Palm theory, wireless networks.

Competencies that will be developed

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/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 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

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.



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).

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