Statistics Mobility Fellowship for Mr Yvo Pokern at Warwick University

Stochastic diffusion processes are used in many different areas of science: as a model for stock markets, train carriage vibrations, weather forecasts and the dynamics of molecules. One aspect of this research deals with how to efficiently simulate diffusion processes when the value of the process is required only at some points in time (e.g. every time a measurement of the physical process is taken), as well as to fit parameters describing these processes to observations from experiment (as in train carriages) or extensive deterministic computer simulation (as in molecular dynamics).It also deals with how to preprocess observational data where this data has qualitatively important features on very fast (femtoseconds) as well as comparatively long (miliseconds) timescales in view of fitting to be performed on the data. In particular, it will deal with the case of noisy time-evolving equations with structures that frequently occur in physical models of mechanical systems.