After a review of the notions of Hausdorff and Fourier dimensions from fractal geometry
and Fourier analysis and the properties of local times of Brownian motion, we study the
Fourier structure of Brownian level sets. ...
Most of the notations and terminological conventions used in this thesis are Statistical.
The aim in risk management is to describe the risk factors present in time series. In order
to group these risk factors, one needs ...