Non-gaussian distributions

摘要

In this work, we study some problems about non-gaussian distributions, “hyper” or “hypo” diffusions where the β order moments are of type tβ/α with β and α belonging to R+∗. We introduce signed measures corresponding to these diffusions on R, inspired by the classical techniques in the brownian case. We examine some specific cases of “hyper” and “hypo” diffusions and we propose a generalization of ITO formula for non-gaussian diffusions. Finally, we give a numerical method based on Discrete Fourier Transforms (DFTs) for the resolution of an “anomalous diffusion equation”.