Cubatures on Wiener space, spatial coalescents, and repulsion-diffusion equations

Thesis

Stochastic models are indispensable in the sciences, but simplifying assumptions are often necessary to retain mathematical or computational tractability. In many cases, this leads to models that are only selectively applicable or exhibit unrealistic behaviour. The guiding philosophy of this thesis is to make an attempt at closing this gap, in two ways: Firstly, by making generic simulation algorithms more efficient, which enables the use of more realistic models that would otherwise be computationally infeasible, across different application areas (Chapter I). And secondly, by building and analysing more realistic generalisations of two common models in the particular field of population biology (Chapters II and III).

Authors: Koepernik, P

• DOI: 10.5287/ora-o8xa6g2no
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: diffusion equation; spatial coalescents; Lambda-coalescent; numerical analysis; Brownian motion; cubatures; Wiener space; Fleming-Viot process; Xi-coalescent; quasi-Monte Carlo; stochastic differential equations
• Subjects: Differential equations, Partial; Stochastic analysis; Population biology--Mathematical models; Stochastic differential equations