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1	Random Polytopes Beermann, Mareen 23 June 2015 (has links) Random polytopes can be constructed in many different ways. In this thesis two certain kinds are considered - random polytopes as the convex hull of random points and as the intersection of finitely many random half spaces. Concerning these two models different issues are treated. Random Polytope Random Tessellation 31.70 - Wahrscheinlichkeitsrechnung 31.50 - Geometrie: Allgemeines ddc:510
2	Limit theorems in preferential attachment random graphs Betken, Carina 17 May 2019 (has links) We consider a general preferential attachment model, where the probability that a newly arriving vertex connects to an older vertex is proportional to a (sub-)linear function of the indegree of the older vertex at that time. We provide a limit theorem with rates of convergence for the distribution of a vertex, chosen uniformly at random, as the number of vertices tends to infinity. To do so, we develop Stein's method for a new class of limting distributions including power-laws. Similar, but slightly weaker results are shown to be deducible using coupling techniques. Concentrating on a specific preferential attachment model we also show that the outdegree distribution asymptotically follows a Poisson law. In addition, we deduce a central limit theorem for the number of isolated vertices. We thereto construct a size-bias coupling which in combination with Stein’s method also yields bounds on the distributional distance. preferential attachment random graphs Stein's method limiting distribution rates of convergence coupling power-law distribution 31.70 - Wahrscheinlichkeitsrechnung ddc:510
3	Randomized integer convex hull Hong Ngoc, Binh 12 February 2021 (has links) The thesis deals with stochastic and algebraic aspects of the integer convex hull. In the first part, the intrinsic volumes of the randomized integer convex hull are investigated. In particular, we obtained an exact asymptotic order of the expected intrinsic volumes difference in a smooth convex body and a tight inequality for the expected mean width difference. In the algebraic part, an exact formula for the Bhattacharya function of complete primary monomial ideas in two variables is given. As a consequence, we derive an effective characterization for complete monomial ideals in two variables. lattice polytopes lattice-free intrinsic volumes mixed multiplicities Bhattacharya function Newton polyhedron complete monomial ideals mean width random lattices integer convex hull random polytopes 31.70 - Wahrscheinlichkeitsrechnung 31.23 - Ideale, Ringe, Moduln, Algebren 13-02 - Research exposition ddc:510
4	Financial Models of Interaction Based on Marked Point Processes and Gaussian Fields / Modellierung von Interaktionseffekten in Finanzdaten mittels Markierter Punktprozesse und Gaußscher Zufallsfelder Malinowski, Alexander 18 December 2012 (has links) No description available. 510 Mathematik Mathematics and Computer Science Markierter Punktprozess Interaktion Transaktionsdaten nicht-ergodisch Tailindex max-stabiler Prozess Peaks-Over-Threshold marked point process mark-location dependence transaction data high-frequency data non-ergodic tail index max-stable process peaks-over-threshold 31.70 Wahrscheinlichkeitsrechnung

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