anomalous diffusions

Grey random fields on the sphere

Grey random fields on the sphere

The research builds on the theory of grey Brownian motion, introduced in the 1990s as a generalization of classical Brownian motion to describe anomalous diffusion phenomena through fractional equations and Mittag-Leffler-type distributions. The goal is to transfer these ideas to the spherical setting, where real-world data, from cosmology (cosmic microwave background radiation) to climatology and geophysics, show significant deviations from Gaussianity, often related to long-range correlations or non-standard distributions.

Stochastic models associated to a Nonlocal Porous Medium Equation

The nonlocal porous medium equation considered in this paper is a degenerate nonlinear evolution equation involving a space pseudo-differential operator of fractional order. This space-fractional equation admits an explicit, nonnegative, compactly supported weak solution representing a probability density function. In this paper we analyze the link between isotropic transport processes, or random flights, and the nonlocal porous medium equation.

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