title: Two-particle anomalous diffusion: probability density functions and self-similar stochastic processes.
abstract: Two-particle dispersion is investigated in the context of anomalous diffusion. Two different modelling approaches related to time subordination are considered and unified in the framework of self-similar stochastic processes. By assuming a single-particle fractional Brownian motion and that the two-particle correlation function decreases in time with a power law, the particle relative separation density is computed for the cases with time sub-ordination directed by a unilateral M-Wright density and by an extremal Lévy stable density. Looking for advisable mathematical properties (for instance, the stationarity of the increments), the corresponding self-similar stochastic processes are represented in terms of fractional Brownian motions with stochastic variance, whose profile is modelled by using the M-Wright density or the Lévy stable density.
authors.affiliation: CRS4, Polaris Building 1, 09010 Pula, Cagliari, Italy.
authors.forename: Gianni
authors.initials: G
authors.lastname: Pagnini
authors.forename: Antonio
authors.initials: A
authors.lastname: Mura
authors.forename: Francesco
authors.initials: F
authors.lastname: Mainardi