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.
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.
|✔ Specialist skills
|Critical thinking skills
|✔ Practical and/or problem-solving skills
The document of each lecture will be uploaded to T2SCHOLA.
|Preliminaries: Measures and Integrals
|Define measures, integrals and probability, and study their fundamental notions
|Random measures, point processes and their distributions
|Define random measures and point processes, and characterize their distributions
|Poisson point processes
|Define the Poisson point processes
|Poisson point processes (continued)
|Reveal some properties of Poisson point processes
|Operations on point processes
|Study some operations on point processes
|Cox point processes and cluster point processes
|Define Cox point processes and cluster point processes, and reveal their properties
|Determinantal point processes
|Define determinantal point processes and reveal their properties
|Define Palm distributions
|Higher order Palm distributions
|Introduce higher order Palm distributions and reveal their properties
|Stationary random measures and stationary point processes
|Reveal some properties of stationary random measures and point processes
|Palm calculus for stationary random measures and point processes
|Study the Palm calculus for stationary random measures and point processes
|Basic formulas in Palm calculus and their applications
|Show some basic properties of stationary point processes using the Palm calculus
|Application to wireless networks
|Introduce a spatial point process model of cellular wireless networks
|Application to wireless networks (continued)
|Derive the coverage probability for cellular network models using various point processes
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.
 F. Baccelli, B. Blaszczyszyn and Mohamed Karray. Random Measures, Point Processes, and Stochastic Geometry. HAL-02460214 (2020)
 G. Last and M. Penrose. Lectures on the Poisson Process. Cambridge University Press, 2017.
Understanding of the related courses above (you do not have to take these courses if you understand the contents of them).