Two-particle anomalous diffusion: probability density functions and self-similar stochastic processes
Copyright policy )Two-particle anomalous diffusion: probability density functions and self-similar stochastic processes
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.
- Ikerbasque Spain
- Alma Mater Studiorum University of Bologna Italy
- University of Siena Italy
- Basque Center for Applied Mathematics Spain
- Polaris Industries United States
generalized grey Brownian motion, fractional Brownian motion, Fractional processes, including fractional Brownian motion, Anomalous diffusion, Lévy stable density, Processes with independent increments; Lévy processes, \(M\)-Wright function, Fractional Brownian motion, M-Wright function, ANOMALOUS DIFFUSION; FRACTIONAL CALCULUS; SELF-SIMILAR STOCHASTIC PROCESSES, self-similar stochastic processes, Stable stochastic processes, anomalous diffusion, Self-similar stochastic processes, Diffusion processes, Generalized grey Brownian motion
generalized grey Brownian motion, fractional Brownian motion, Fractional processes, including fractional Brownian motion, Anomalous diffusion, Lévy stable density, Processes with independent increments; Lévy processes, \(M\)-Wright function, Fractional Brownian motion, M-Wright function, ANOMALOUS DIFFUSION; FRACTIONAL CALCULUS; SELF-SIMILAR STOCHASTIC PROCESSES, self-similar stochastic processes, Stable stochastic processes, anomalous diffusion, Self-similar stochastic processes, Diffusion processes, Generalized grey Brownian motion
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