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Marked particle processes
Kovář, Matěj ; Pawlas, Zbyněk (advisor) ; Beneš, Viktor (referee)
This diploma thesis delves into the study of marked particle processes, a relatively unexplored field in stochastic geometry and spatial statistics. The main aim of the thesis is to lay some basic foundations of the marked particle processes and to present a suitable second-order characteristic that would appropriately evaluate an interaction between particles and corresponding marks. A primary focus is devoted to introducing the notion of the particle-weighted f-mark correlation function defined via standard second- order factorial measure. The thesis presents some of the potential marked particle process models and some of the forms of the particle-weighted f-mark correlation function. In the last two chapters the simulation study discussing the models and its f-mark correlation function is presented. 1

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