Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Referee "Sturm, Anja Prof. Dr."
Now showing items 114 of 14

A Central Limit Theorem for Functions on Weighted Sparse Inhomogeneous Random Graphs
(20230713)We prove a central limit theorem for a certain class of functions on weighted sparse inhomogeneous random graphs. The proof uses a perturbative form of Stein's method and relies on a careful analysis of the local structure ... 
The contact process in an evolving random environment
(20211126)Recently, there has been an increasing interest in interacting particle systems on evolving random graphs, respectively in time evolving random environments. In this thesis a contact process in a time evolving edge random ... 
Random Function Iterations for Stochastic Feasibility Problems
(20190321)The aim of this thesis is to develop a theory that describes errors in fixed point iterations stochastically, treating the iterations as a Markov chain and analyzing them for convergence in distribution. These particular ... 
Empirical Optimal Transport on Discrete Spaces: Limit Theorems, Distributional Bounds and Applications
(20190109)Optimal Transport and especially distances based on optimal transport are a widely applied tool in different mathematical disciplines. Among others it is used in probability theory to study for example limit laws or derive ... 
Shape space in terms of Wasserstein geometry and application to quantum physics
(20181126)This thesis offers a mathematical framework to treat quantum dynamics without reference to a background structure, but rather by means of the change of the shape of the state. For this, Wasserstein geometry is used. The ... 
Algorithms for structured nonconvex optimization: theory and practice
(20180724)We first synthesize and unify notions of regularity, both of individual functions/sets and of families of functions/sets, as they appear in the convergence theory of fixed point iterations. Several new primal and dual ... 
Dualities and genealogies in stochastic population models
(20180226)In the thesis, population processes are studied in two different settings. In Part I, which arose in collaboration with Dr. Jan Swart, a socalled cooperative branching process is considered. We construct this process ... 
Convergence Rates in Dynamic Network Models
(20180223)The stochastic network model by Britton and Lindholm (Journal of Statistical Physics 3, 2010) describes a class of reasonably realistic dynamics for a complex system with an underlying network structure. In a closed social ... 
On two Random Models in Data Analysis
(20170302)In this thesis, we study two random models with various applications in data analysis. For our first model, we investigate subspaces spanned by biased random vectors. The underlying random model is motivated by applications ... 
Convergence of the Genealogy of the Spatial Cannings Model
(20161116)In this thesis we consider the genealogy of a spatial Cannings model. This is a population model in which individuals are distributed over a countable set of sites G. The reproduction of individuals at each site is ... 
Stochastic Models in Population Genetics: The Impact of Selection and Recombination
(20150327)We consider gene genealogies from populations under selective pressure and take into account that genes can be reassembled during the reproduction process due to recombination. The main result is the derivation of an ... 
BrownResnick Processes: Analysis, Inference and Generalizations
(20130125)This thesis deals with the analysis, inference and further generalizations of a rich and flexible class of maxstable random fields, the socalled BrownResnick processes. The first chapter gives the ... 
Pathwise Uniqueness of the Stochastic Heat Equation with Hölder continuous o diffusion coefficient and colored noise
(20130115)We consider the stochastic heat equation in $\mathbb{R}_+ \times \mathbb{R}^q$ with multiplicative noise: \[ \partial_t u(t,x) = \frac{1}{2} \Delta u(t,x) + b(t,x,u(t,x)) + \sigma(t,x,u(t,x)) \, \dot{W}(t,x) .\] Here, ... 
Julia Set as a Martin Boundary
(20101118)The Julia set of the class of hyperbolic rational maps having a totally disconnected Julia set is here identified as the Martin boundary of a Markov chain by using symbolic dynamics. When ...