This conference is part of the MAST Lecture Series organised by the Mathematics Department of the University of Luxembourg with the support of the FNR. The objective is to share the most recent developments of mathematics and their applications in the Luxembourg scientific community.
Abstract
Variations are a standard tool in analysis and integration theory. While they are often used to study path properties of a function or to compute the fractional dimension, they are also extremely important in statistics and probability. In this talk we will review some statistical theory for diffusion processes, which is heavily based upon the probabilistic analysis of the so called power variations and their extensions. We will highlight numerous estimating and testing procedures, which gained popularity in financial applications. We further demonstrate possible extensions of the asymptotic theory to fractional models.