Multiple Markov properties for fractional parabolic SPDEs

Spatiotemporal stochastic processes have applications in various fields, but they can be difficult to numerically approximate in a reasonable time, in particular, in the context of statistical inference for large datasets. <br/>Recently, a new approach for efficient spatiotemporal statistical modeling has been proposed, where the space-time...

A semi-group approach to the thin-film equation with general mobility

This thesis treats the thin-film equation which models the film height $h$ for a viscous film in the complete wetting regime. We show existence and uniqueness to the thin-film equation with mobility m(h) = hⁿ and mobility exponent n∈ (1,3/2)∪ (3/2,3). The thin-film equation is rewritten as an abstract Cauchy problem and usage of semi...

Gradient flow and quantum Markov semigroups with detailed balance

In this thesis we present a study of quantum Markov semigroups. In particular, we mainly consider quantum Markov semigroups with detailed balance that are defined on finite-dimensional C*-algebras. They have an invariant density matrix ρ. Carlen and Maas showed that the evolution on the set of invertible density matrices that is given by such a...

Generation of wavelets by semigroups

Wavelets are a recent development in signal processing. These kind of functions<br/>are both well-localized in time and in frequency, and so using these to transform the signal gives insight where certain frequencies are needed. The classical way of constructing wavelets, as described by Daubechies and Meyer [3,9] is only well-suited for the...

Topological Extensions of Holomorphic Functional Calculus for Sectorial and Half-plane Type Operators

The theory of functional calculus deals with the idea of 'inserting operators into functions'. The holomorphic (or Dunford-Riesz) functional calculus is based on a class of functions can be represented by the Cauchy-integral formula. A topological extension means that the primary calculus is extended to a wider class of functions and the...