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• #### A Central Limit Theorem for Functions on Weighted Sparse Inhomogeneous Random Graphs ﻿

(2023-07-13)
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 ﻿

(2021-11-26)
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 ...
• #### Dualities and genealogies in stochastic population models ﻿

(2018-02-26)
In the thesis, population processes are studied in two different settings. In Part I, which arose in collaboration with Dr. Jan Swart, a so-called cooperative branching process is considered. We construct this process ...
• #### Convergence of the Genealogy of the Spatial Cannings Model ﻿

(2016-11-16)
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 ﻿

(2015-03-27)
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 ...
• #### Pathwise Uniqueness of the Stochastic Heat Equation with Hölder continuous o diffusion coefficient and colored noise ﻿

(2013-01-15)
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, ...