连续时间随机游动的多点分布函数
Multi-point Distribution Function for the Continuous Time Random Walk
摘要：
本文导出了连续时间随机游动（CTRW）的两点分布函数$p(x_1,t_1;x_2,t_2)$的Fourier-Laplace变换的显式表达式，从而推广了Montroll和Weiss关于单点分布函数$p(x_1,t_1)$的结果.多点分布函数具有Montroll-Weiss CTRW和老化CTRW单点分布函数的卷积的结构。利用连续极限下的无偏CTRW，研究了多时空分数阶扩散方程[Baule and Friedrich [{ \em Europhysics Letters} { \bf 77} 10002（2007）]的随机游走基础.
英文摘要：
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.
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