Subordination Pathways to Fractional Diffusion

Abstract

The uncoupled Continuous Time Random Walk (CTRW) in one space-dimension and under power law regime is splitted into three distinct random walks: (rw_1), a random walk along the line of natural time, happening in operational time; (rw_2), a random walk along the line of space, happening in operational time;(rw_3), the inversion of (rw_1), namely a random walk along the line of operational time, happening in natural time. Via the general integral equation of CTRW and appropriate rescaling, the transition to the diffusion limit is carried out for each of these three random walks. Combining the limits of (rw_1) and (rw_2) we get the method of parametric subordination for generating particle paths, whereas combination of (rw_2) and (rw_3) yields the subordination integral for the sojourn probability density in space-time fractional diffusion.

20 pages, 4 figures

References in corpus (5)

• Fractional Calculus: Integral and Differential Equations of Fractional Order
• The fundamental solution of the space-time fractional diffusion equation
• Continuous Time Random Walks (CTRWs): Simulation of continuous trajectories
• Mittag-Leffler Waiting Time, Power Laws,Rarefaction, Continuous Time Random Walk, Diffusion Limit
• Continuous time random walk, Mittag-Leffler waiting time and fractional diffusion: mathematical aspects