Modul

The module will be completed by an oral exam (ca. 30 min).

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.

none

• 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

The contents of the module Probability Theory are recommended.

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