耦合Lévy过程中的Moses，Noah和Joseph效应
Moses, Noah and Joseph Effects in Coupled Lévy Processes
摘要：
我们研究了一种方法，用于检测异常扩散的起源，当它被观察到在一个合奏的时间序列，实验或数值生成的，没有知识的确切的基本动力学。均方位移的异常扩散标度的原因被分解为三个根本原因：增量相关性由“约瑟夫效应”表示[Mandelbrot 1968]，增量概率密度的厚尾导致“诺亚效应”[Mandelbrot 1968]，非平稳性导致“摩西效应”[Chen et al. 2017]。在适当的重新缩放后，基于这些效应的量化，增量分布在增加的时间收敛到时不变的渐近形状。对于不同的过程，这个渐近极限可以是一个平衡态，一个无穷不变的，或一个无穷协变的密度。我们使用时间序列分析的数值方法来量化一个非线性耦合的Lévy行走模型中的三个影响，比较我们的结果与理论预测，并讨论了该方法的一般性。
英文摘要：
We study a method for detecting the origins of anomalous diffusion, when it is observed in an ensemble of times-series, generated experimentally or numerically, without having knowledge about the exact underlying dynamics. The reasons for anomalous diffusive scaling of the mean-squared displacement are decomposed into three root causes: increment correlations are expressed by the "Joseph effect" [Mandelbrot 1968], fat-tails of the increment probability density lead to a "Noah effect" [Mandelbrot 1968], and non-stationarity, to the "Moses effect" [Chen et al. 2017]. After appropriate rescaling, based on the quantification of these effects, the increment distribution converges at increasing times to a time-invariant asymptotic shape. For different processes, this asymptotic limit can be an equilibrium state, an infinite-invariant, or an infinite-covariant density. We use numerical methods of time-series analysis to quantify the three effects in a model of a non-linearly coupled Lévy walk, compare our results to theoretical predictions, and discuss the generality of the method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
