Two-particle anomalous diffusion: probability density functions and self-similar stochastic processes

作者：Pagnini Gianni; Mura Antonio; Mainardi Francesco^*

来源：Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences, 2013, 371(1990): 20120154.

DOI：10.1098/rsta.2012.0154

• anomalous diffusion
• self-similar stochastic processes
• fractional Brownian motion
• generalized grey Brownian motion
• M-Wright function
• Levy stable density

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 subordination directed by a unilateral M-Wright density and by an extremal Levy 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 Levy stable density.

• 出版日期2013-5-13