Multi-point Distribution Function for the Continuous Time Random Walk

Abstract

We derive an explicit expression for the Fourier-Laplace transform of the two-point distribution function $p(x_1,t_1;x_2,t_2)$ of a continuous time random walk (CTRW), thus generalizing the result of Montroll and Weiss for the single point distribution function $p(x_1,t_1)$. The multi-point distribution function has a structure of a convolution of the Montroll-Weiss CTRW and the aging CTRW single point distribution functions. The correlation function $<x(t_1)x(t_2)>$ for the biased CTRW process is found. The random walk foundation of the multi-time-space fractional diffusion equation [Baule and Friedrich [{\em Europhysics Letters} {\bf 77} 10002 (2007)] is investigated using the unbiased CTRW in the continuum limit.

7 pages

References in corpus (2)

• A fractional diffusion equation for two-point probability distributions of a continuous-time random walk
• Strong Correlations Between Fluctuations and Response in Aging Transport

Cited by in corpus (1)

• Continuous Time Random Walks (CTRWs): Simulation of continuous trajectories