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We describe a prototype approach to flexible modelling for maxima observed at sites in a spatial domain, based on fitting of max-stable processes derived from underlying Gaussian random fields. The models we propose have generalised extreme-value marginal ...
The important task of evaluating the impact of random parameters on the output of stochastic ordinary differential equations (SODE) can be computationally very demanding, in particular for problems with a high-dimensional parameter space. In this work we c ...
The modelling of prey-predator interactions is of major importance for the understanding of population dynamics. Classically, these interactions are modelled using ordinary differential equations, but this has the drawbacks of assuming continuous populatio ...
We propose certified reduced basis methods for the efficient and reliable evaluation of a general output that is implicitly connected to a given parameterized input through the harmonic Maxwell's equations. The truth approximation and the development of th ...
We present the Walsh theory of stochastic integrals with respect to martingale measures, and various extensions of this theory, alongside of the Da Prato and Zabczyk theory of stochastic integrals with respect to Hilbert-space-valued Wiener processes, and ...
Identification of kinetic models is essential for monitoring, control and optimization of industrial processes. Robust kinetic models are often based on first-principles and described by differential equations. Identification of reaction kinetics, namely r ...
Researchers and developers typically use I-V curves (current vs. potential) as a means to demonstrate good data fitting of a model under experimental validation. Despite the popularity of this method, assessment of the results can be intuitive rather than ...
In this thesis we investigate different ways of approximating the solution of the chemical master equation (CME). The CME is a system of differential equations that models the stochastic transient behaviour of biochemical reaction networks. It does so by d ...
In this paper we consider reduced basis approximation and a posteriori error estimation for linear functional outputs of affinely parametrized linear and non-linear parabolic partial differential equations. The essential ingredients are Galerkin projection ...
A fine term structure models have gained significant attention in the finance literature, mainly due to their analytical tractability and statistical flexibility. The aim of this article is to present both theoretical foundations as well as empirical aspec ...