On Hilfer's objection to the fractional time diffusion equation
On Hilfer's objection to the fractional time diffusion equation
复制标题
论希尔弗对分数时间扩散方程的反对
DOI：
10.1016/j.physa.2006.05.022
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
I. Sokolov
中科院分区：
文献类型：
--
作者：
E. Barkai;I. Sokolov
Hilfer [Physica A 329（2003）35]声称给出了一个具有长尾等待时间概率密度的连续时间随机游走（CTRW）模型的例子，该模型在连续极限中接近高斯行为。严格的极限定理，推导出以前，然而，在长时间的限制，这样的CTRW收敛到一个非高斯行为。讨论了CTRW模型的两种连续极限：分数阶连续极限和Hilfer提出的连续极限。我们表明，分数的限制产生正确的长时间的CTRW的行为，而Hilfer的连续极限没有。我们讨论了一个一般的方法来找到一个连续极限的CTRW过程。
Hilfer [Physica A 329 (2003) 35] claims to give an example of a continuous time random walk (CTRW) model with long-tailed waiting time probability density that approaches a Gaussian behavior in the continuum limit. Rigorous limit theorems, derived previously, show however that in the limit of long-time such a CTRW converges to a non-Gaussian behavior. We discuss two types of continuum limits for the CTRW model: the fractional continuum limit and the one introduced by Hilfer. We show that the fractional limit yields the correct long-time behavior of the CTRW, while Hilfer's continuum limit does not. We discuss a general approach to find a continuum limit of the CTRW process.