Discipline: 
Mathematics
Status: 
Available
Level: 
Masters Project
Level: 
Honours Project
Supervisor(s): 
Dr Thomas Taimre

A diffusion process on a Riemannian manifold has infinitesimal generator which is fundamentally related to the Laplace--Beltrami operator on that manifold.  For a given manifold, it is possible to simulate sample paths of such a diffusion process, and the most likely path for a diffusion process can be determined by using the Onsager--Machlup function.  

This project focuses on developing importance sampling schemes by continuously mapping the diffusion (thereby continuously varying its infinitesimal generator), where the mapping may depend on the entire sample path history.  An example would be continuously diverting sample paths toward the most likely path conditional on an event of interest.