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Medientyp:
E-Artikel
Titel:
Two-particle anomalous diffusion: probability density functions and self-similar stochastic processes
Beteiligte:
Pagnini, Gianni;
Mura, Antonio;
Mainardi, Francesco
Erschienen:
The Royal Society, 2013
Erschienen in:
Philosophical Transactions: Mathematical, Physical and Engineering Sciences, 371 (2013) 1990, Seite 1-11
Sprache:
Englisch
DOI:
10.1098/rsta.2012.0154
ISSN:
1364-503X
Entstehung:
Anmerkungen:
Beschreibung:
<p>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 selfsimilar stochastic processes. By assuming a singleparticle 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 subordination 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 selfsimilar 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.</p>