A class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics
Abstract
In this paper we present a general mathematical construction that allows us to define a parametric class of -sssi stochastic processes (self-similar with stationary increments), which have marginal probability density function that evolves in time according to a partial integro-differential equation of fractional type. This construction is based on the theory of finite measures on functional spaces. Since the variance evolves in time as a power function, these -sssi processes naturally provide models for slow and fast anomalous diffusion. Such a class includes, as particular cases, fractional Brownian motion, grey Brownian motion and Brownian motion.
Keywords
Cite
@article{arxiv.0711.0665,
title = {A class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics},
author = {Antonio Mura and Francesco Mainardi},
journal= {arXiv preprint arXiv:0711.0665},
year = {2007}
}
Comments
14 pages, 1 figure, Presented at GF07: Linear and Non-linear Theory of Generalized Functions and Its Applications, The Banach center Bedlewo, Poland, Seprember 2-8 2007