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Modul
Poisson Processes [M-MATH-102922]
Credits
5Recurrence
UnregelmäßigDuration
1 SemesterLanguage
Level
4Version
1Responsible
Organisation
- KIT-Fakultät für Mathematik
Part of
Bricks
Identifier | Name | LP |
---|---|---|
T-MATH-105922 | Poisson Processes | 5 |
Competence Certificate
The module will be completed by an oral exam (ca. 30 min).
Competence Goal
The students know about important properties of the Poisson process. The focus is on probabilistic methods and results which are independent of the specific phase space. The students understand the central role of the Poisson process as a specific point process and as a random measure.
Prerequisites
none
Content
- The Poisson process as particular point process
- Multivariate Mecke equation
- Superpositions, markings and thinnings
- Characterizations of the Poisson process
- Stationary Poisson and point processes
- Balanced allocations and the Gale-Shapley algorithm
- Compound Poisson processes
- Wiener-Ito integrals
- Fock space representation
Recommendation
The contents of the module Probability Theory are recommended.
Workload
Total workload: 150 hours
Attendance: 60 hours
- lectures, problem classes, and examination
Self-studies: 90 hours
- follow-up and deepening of the course content,
- work on problem sheets,
- literature study and internet research relating to the course content,
- preparation for the module examination