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.
Two-particle anomalous diffusion: Probability density functions and self-similar stochastic processes / G. Pagnini; A. Mura; Francesco MAINARDI. - In: PHILOSOPHICAL TRANSACTIONS - ROYAL SOCIETY. MATHEMATICAL, PHYSICAL AND ENGINEERING SCIENCES. - ISSN 1471-2962. - STAMPA. - 371:1990(2013), pp. ID 2012.0154.1-ID 2012.0154.11. [10.1098/rsta.2012.0154]
Two-particle anomalous diffusion: Probability density functions and self-similar stochastic processes
MURA, ANTONIO;MAINARDI, FRANCESCO
2013
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.