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National Repository of Grey Literature 2 records found  Search took 0.02 seconds. 
Random measurable sets and particle processes
 Jurčo, Adam ; Rataj, Jan (advisor) ; Beneš, Viktor (referee)
Random measurable sets and particle processes Adam Jurčo Abstract In this thesis we deal with particle processes on more general spaces. First we in- troduce the space of Lebesgue measurable sets represented by indicator functions with topology given by L1 loc convergence. We the explore the topological properties of this space and its subspaces of sets of finite and locally finite perimeter. As these spaces do not satisfy the usual topological assumptions needed for construction of point processes we use another approach based on measure-theoretic assumptions. This will allow us to define point processes given by finite dimensional distributions on measurable subsets of the space of Lebesgue-measurable sets. Then we will derive a formula for a volume fraction of a Boolean process defined in this more general setting. Further we introduce a Boolean process with particles of finite perimeter and derive a formula for its specific perimeter. 1
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Existence and uniqueness of the distribution of a random measure given by finite dimensional projections
 Jurčo, Adam ; Rataj, Jan (advisor) ; Pawlas, Zbyněk (referee)
Title: Existence and uniqueness of the distribution of a random measure given by finite dimensional projections Author: Adam Jurčo Department: Department of Probability and Mathematical Statistics Supervisor: prof. RNDr. Jan Rataj, CSc., Department of Probability and Mathe- matical Statistics Abstract: This thesis deals with the existence and uniqueness of the distribu- tion of a random measure given a system of finite-dimensional distributions. A random measure can be interpreted as a particular system of random variables. Conversely, we will want to know what conditions would allow a system of random variables to be extended to a random measure and if this extension is unique. We will start with a consistent system of finite-dimensional distributions and use Daniell-Kolmogorov theorem to find the necessary and sufficient conditions for the existence of such extension. A counterexample will be included to show that it is not possible to use this theory for random signed measures. Keywords: Random measure, point process, finite-dimensional distributions. 1
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See also: similar author names
2 Jurčo, Andrej
1 Jurčo, Antonín
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