Non-Gaussian distributions. (English) Zbl 0930.65004
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.
Reviewer: N.Curteanu (Iaşi)
MSC:
| 65C50 | Other computational problems in probability (MSC2010) |
| 60J60 | Diffusion processes |
Keywords:
non-Gaussian distributions; non-Gaussian diffusions; hypo-diffusion; hyper-diffusion; non-Gaussian diffusion processesReferences:
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