Abstract
We derive an explicit expression for the Fourier–Laplace transform of the two-point distribution function p(x1, t1; x2, t2) of a continuous time random walk (CTRW), thus generalizing the result of Montroll and Weiss for the single-point distribution function p(x1, t1). The multi-point distribution function has a structure of a convolution of the Montroll–Weiss CTRW and the ageing CTRW single-point distribution functions. The correlation function \langle x(t_1) x(t_2) \rangle for the biased CTRW process is found. The random walk foundation of the multi-time–space fractional diffusion equation is investigated using the unbiased CTRW in the continuum limit.
Original language | American English |
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Journal | Journal of Statistical Mechanics: Theory and Experiment |
State | Published - 2007 |