Time and Place

Lecture

Thursday, 8:15 - 9:55, E20, Heho 18 (Start: 14.4.)

Exercise Session

Tuesday, 16:15 - 17:55, 2003, O28 (Start: 26.4.)

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Type

2 hours lecture + 1 hours exercise classes

4 credit points

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Prerequisites

Basic knowledge of probability like taught in "Elementare Wahrscheinlichkeitsrechnung und Statistik".

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Content

Stochastic Geometry is a branch of probability theory dealing with random geometric structures. There are three basic concepts in stochastic geometry: Point processes, random closed sets and random fields. In order to avoid overlap with other lecturs, we will concentrate on random closed sets.

Of particular interest will be germ grain models, i.e. random closed sets that arise as unions of random compact sets.

The topics of the lecture will be:

• Random closed sets as random variables in the space of closed sets (measure-theoretic definition; properties of the space of closed sets).
• Germ grain models: Definition, elementary properties and selected models.
• Quantitative description of random closed sets and in particular germ grain models.

In the winter term there will be a second part of this lecture, where we will treat random compact sets and random tessallations.

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Exam

There is no prerequisite. Further details will be announced later. 

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Exercise sheets

Submitting solutions for the exercise sheets is strongly recommanded.

 

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Literature

• Schneider, R. and Weil, W.: Stochastic and Integral Geometry. Springer, 2008.
• Mecke, K. and Stoyan, D.: Morphology of Condensed Matter. Springer, 2002.
• Molchanov, I.: Theory of Random Sets. Springer, 2005.
• (Chiu, S.,) Stoyan, D., Kendall, W. and Mecke, J.: Stochastic Geometry and its applications. Wiley, 1995, 2008, 2013.
• Spodarev, E.: Stochastic geometry, spatial statistics and random fields. Springer, 2013.