论文标题
摩西，诺亚和约瑟夫在耦合的莱维过程中的效果
Moses, Noah and Joseph Effects in Coupled Lévy Processes
论文作者
论文摘要
我们研究了一种检测异常扩散的起源的方法，当它在时间序列的集合中观察到，该方法是通过实验或数值生成的，而无需了解确切的基本动力学。 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]。经过适当的重新缩放后，基于对这些效应的定量，增量分布在增加的时间收敛到时间不变的渐近形状。对于不同的过程，这种渐近极限可以是平衡状态，无限不变或无限范围的密度。我们使用时间序列分析的数值方法来量化非线性耦合Lévy步行模型中的三个效果，将我们的结果与理论预测进行比较，并讨论该方法的一般性。
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.
