延迟解耦连续时间随机游动不提供电报方程的模型
The delayed uncoupled continuous-time random walks do not provide a model for the telegraph equation
摘要：
有几篇论文声称，所谓的延迟连续时间随机游动（DCTRW）在微观水平上为一维电报方程提供了一个模型。这个结论现在很普遍，但很奇怪，因为电报方程描述的是有限传播速度的现象，而粒子在DCTRW中的运动速度是无限的。在本文中，我们调查如何准确的近似所提供的电报方程的DCTRW。我们表明，扩散方程，是正确的限制的DCTRW，给出更好的近似在$L_2$范数的DCTRW比电报方程。因此，我们的结论是，第一，DCTRW不提供任何正确的微观解释的一维电报方程，第二，动力学（精确）模型的电报方程是不同的模型的基础上的DCTRW。
英文摘要：
It has been alleged in several papers that the so called delayed continuous-time random walks (DCTRWs) provide a model for the one-dimensional telegraph equation at microscopic level. This conclusion, being widespread now, is strange, since the telegraph equation describes phenomena with finite propagation speed, while the velocity of the motion of particles in the DCTRWs is infinite. In this paper we investigate how accurate are the approximations to the DCTRWs provided by the telegraph equation. We show that the diffusion equation, being the correct limit of the DCTRWs, gives better approximations in $L_2$ norm to the DCTRWs than the telegraph equation. We conclude therefore that, first, the DCTRWs do not provide any correct microscopic interpretation of the one-dimensional telegraph equation, and second, the kinetic (exact) model of the telegraph equation is different from the model based on the DCTRWs.
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