- Basic concepts of the theory of spatial point processes (marking, intensity measure, ...),
- Multidimensional Poisson process, Poisson Cluster processes,
- Basic concepts of the theory of random closed sets,
- Germ-grain models, in particular the Boolean model,
- Random mosaics.
Stochastic Geometry (M, 4.5 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-62-18-M-7||Stochastic Geometry||4.5 CP (135 h)|
|CP, Effort||4.5 CP = 135 h|
|Position of the semester||1 Sem. irreg.|
|Level|| Master (Advanced)|
|Area of study||[MAT-STO] Stochastics/Statistics/Financial Mathematics|
|Reference course of study||[MAT-88.105-SG] M.Sc. Mathematics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
|P||42 h||93 h||-||-||PL1||4.5||irreg.|
- About [MAT-62-18-K-7]: Title: "Stochastic Geometry"; Presence-Time: 42 h; Self-Study: 93 h
Examination achievement PL1
- Form of examination: oral examination (20-30 Min.)
- Examination Frequency: each semester
- Examination number: 86407 ("Stochastic Geometry")
Evaluation of grades
The grade of the module examination is also the module grade.
Competencies / intended learning achievements
Upon successful completion of this module, the students have learnt some of the most important concepts and models of the theory of spatial point processes and the theory of random closed sets. They are able to name the important statements of the lecture, classify and explain the illustrated relationships. They understand the proofs presented in the lecture and are able to comprehend and explain them. In particular, they are able to outline the conditions and assumptions that are necessary for the validity of statements.
- D. Stoyan, W. S. Kendall, J. Mecke: Stochastic Geometry and its Applications,
- R. Schneider, W. Weil: Stochastic and Integral Geometry.
Requirements for attendance (informal)
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-60-11-M-4] Probability Theory (M, 9.0 LP)
Requirements for attendance (formal)