2019 Applied Probability

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Academic unit or major
Graduate major in Mathematical and Computing Science
Instructor(s)
Miyoshi Naoto  Nakano Yumiharu 
Course component(s)
Lecture
Day/Period(Room No.)
Mon7-8(W832)  Thr7-8(W832)  
Group
-
Course number
MCS.T410
Credits
2
Academic year
2019
Offered quarter
3Q
Syllabus updated
2019/9/27
Lecture notes updated
2019/11/18
Language used
Japanese
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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 cellular wireless networks.

Student learning outcomes

At the end of this course, students will be able to understand the theory of point processes, one of the fundamental class of stochastic processes, and apply it to modeling and performance evaluation of cellular wireless networks.

Keywords

Point processes, Poisson processes, cox processes, stationary point processes, Palm theory, cellular wireless networks, coverage probability.

Competencies that will be developed

Intercultural skills Communication skills Specialist skills Critical thinking skills Practical and/or problem-solving skills
- - -

Class flow

Lectures with a blackboard. The document of each lecture will be uploaded to the OCW-i.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Preliminaries: Measures and Integrals Define measures, integrals and probability
Class 2 Point processes and their intensity measures Define point processes and their intensity measures
Class 3 Distribution of point processes Characterize the probability distribution of point processes
Class 4 Poisson point processes Define the Poisson point processes
Class 5 Some properties of Poisson point processes Reveal some properties of Poisson point processes
Class 6 Random measures and Cox point processes Define random measures and Cox point processes
Class 7 Determinantal point processes Define determinantal point processes
Class 8 Stationary point processes Reveal some properties of stationary point processes
Class 9 Marked point processes and Palm probability Define marked point processes and the Palm probability measure
Class 10 Basic formulas of Palm theory Show some basic formulas of Palm theory
Class 11 Basic properties of stationary point processes Show some basic properties of stationary point processes using the Palm calculus
Class 12 Application to cellular networks Introduce the spatial point process model of cellular wireless networks
Class 13 Coverage probability of a cellular network model: The case of a Poisson-based model Derive the coverage probability of Poisson-based model of cellular networks
Class 14 Coverage probability of a cellular network model: The cases of non-Poisson based models Derive the coverage probability of non-Poisson-based model of cellular networks
Class 15 TBA TBA

Textbook(s)

None.

Reference books, course materials, etc.

[1] F. Baccelli and B. Blaszczyszyn. "Stochastic geometry and wireless networks, Volume I: Theory." Foundations and Trends in Networking, vol. 3, pp. 249-449, 2009.
[2] F. Baccelli and B. Blaszczyszyn. "Stochastic geometry and wireless networks, Volume II: Applications." Foundations and Trends in Networking, vol. 4, pp. 1-312, 2009.
[3] D. J. Daley and D. Vere-Jones. An Introduction to the Theory of Point Processes, Volume I: Elementary Theory and Methods. Springer, 2003.
[4] D. J. Daley and D. Vere-Jones. An Introduction to the Theory of Point Processes, Volume II: General Theory and Structure. Springer, 2008.
[5] G. Last and M. Penrose. Lectures on the Poisson Process. Cambridge University Press, 2017.

Assessment criteria and methods

Reports.

Related courses

  • MCS.T212 : Fundamentals of Probability
  • MCS.T312 : Markov Analysis

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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