Non-Gaussian distributions (Q1294244)

The paper studies (non-Gaussian) diffusions classified as either ``hypo-diffusion'' or ``hyper-diffusion'', where the \(\beta\) order moments are of the type \(t^{\beta/\alpha}\), with \(\beta\) and \(\alpha\) belonging to \(\mathbb{R}^*_+\). The authors introduce signed measures corresponding to non-Gaussian diffusions on \(\mathbb{R}\), inspired by the classical techniques in the Brownian case. Specific situations of hyper- and hypo-diffusions are analyzed, and a generalization of the Ito formula for non-Gaussian diffusions is proposed. A numerical method is presented based on the discrete Fourier transform for the resolution of a so-called ``anomalous diffusion equation''. The corresponding algorithms and numerical computations provide a better understanding of the various cases involved within the non-Gaussian diffusion processes.