Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-62-18-M-7

Stochastic Geometry (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-62-18-M-7 Stochastic Geometry 4.5 CP (135 h)

Basedata

CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
Area of study [MAT-STO] Stochastics/Statistics/Financial Mathematics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V+1U MAT-62-18-K-7
Stochastic Geometry
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.


Contents

  • 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.

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.

Literature

  • D. Stoyan, W. S. Kendall, J. Mecke: Stochastic Geometry and its Applications,
  • R. Schneider, W. Weil: Stochastic and Integral Geometry.

Requirements for attendance (informal)

Modules:

Requirements for attendance (formal)

None

References to Module / Module Number [MAT-62-18-M-7]

Module-Pool Name
[MAT-62-MPOOL-7] Specialisation Statistics (M.Sc.)
[MAT-65-MPOOL-7] Specialisation Image Processing and Data Analysis (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)
[MAT-RM-MPOOL-7] Pure Mathematics (Advanced Modules M.Sc.)