CRS4, Polaris Building 1, 09010 Pula, Cagliari, Italy.
Philos Trans A Math Phys Eng Sci. 2013 Apr 1;371(1990):20120154. doi: 10.1098/rsta.2012.0154. Print 2013 May 13.
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.
本文研究了反常扩散背景下的双粒子弥散。考虑了两种不同的与时间次定相关的建模方法，并在自相似随机过程的框架内统一起来。通过假设单粒子分数布朗运动和双粒子相关函数随时间以幂律衰减，计算了在时间次定由单边 M-Wright 密度和极值 Lévy 稳定密度引导的情况下的粒子相对分离密度。为了寻找合理的数学性质（例如，增量的平稳性），相应的自相似随机过程用具有随机方差的分数布朗运动表示，其轮廓通过使用 M-Wright 密度或 Lévy 稳定密度进行建模。
