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Random closed sets
Stroganov, Vladimír ; Honzl, Ondřej (advisor) ; Rataj, Jan (referee)
In this bachelor thesis we are concerned with basic knowledge in random set theory. We define here such terms, as capacity functional, se- lection, measurable and integrable multifunction, Castaing representation and Aumann expectation of random closed set. We present Choquet theo- rem, Himmelberg measurability theorem, theorems of properties of selections and expectation. We present also several examples which illustrate the the- ory. 1
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Random closed sets
Stroganov, Vladimír ; Honzl, Ondřej (advisor) ; Rataj, Jan (referee)
In this bachelor thesis we are concerned with basic knowledge in random set theory. We define here such terms, as capacity functional, se- lection, measurable and integrable multifunction, Castaing representation and Aumann expectation of random closed set. We present Choquet theo- rem, Himmelberg measurability theorem, theorems of properties of selections and expectation. We present also several examples which illustrate the the- ory. 1
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Simulation of point processes
KOPECKÝ, Jiří
The aim of the thesis is to create a pack of functions in Wolfram Mathematica software to simulate spatial point patterns of chosen hard-core and Gibbs processes. Then it tries to apply these models to real data, estimate the parameters of models for real data and test the validity of models. The thesis can serve as introduction into the theory of spatial point processes.
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