超极端事件对Weierstrass-Mandelbrot连续时间随机游动的影响
Super-extreme event's influence on a Weierstrass-Mandelbrot Continuous-Time Random Walk
摘要：
考虑了超极值事件对速度自相关函数（VAF）影响的两种极限情况。VAF本身是在分级Weierstrass-Mandelbrot连续时间随机游走（WM-CTRW）形式主义中推导出来的，该形式主义能够覆盖广泛的连续时间随机游走。首先，我们研究了持续漂移形式的超极端事件，其持续时间比任何其他事件都要长。其次，我们考虑了一个超级极端事件的冲击形式的大小和速度远远大于那些对应于任何其他事件。我们发现，这些超级极端事件的出现大大改变了由WM-CTRW过程内生的极端事件（所谓的“黑天鹅”）所确定的结果。例如，在后一种情况下，VAF的变化是以某种不稳定的形式出现的，并且与前一种情况下引起的变化明显不同。在每种情况下，这些变化与没有超级极端事件的情况相比都有很大的不同，这表明如果发生超级极端事件，就有可能在自然系统中检测到它们。
英文摘要：
Two utmost cases of super-extreme event's influence on the velocity autocorrelation function (VAF) were considered. The VAF itself was derived within the hierarchical Weierstrass-Mandelbrot Continuous-Time Random Walk (WM-CTRW) formalism, which is able to cover a broad spectrum of continuous-time random walks. Firstly, we studied a super-extreme event in a form of a sustained drift, whose duration time is much longer than that of any other event. Secondly, we considered a super-extreme event in the form of a shock with the size and velocity much larger than those corresponding to any other event. We found that the appearance of these super-extreme events substantially changes the results determined by extreme events (the so called "black swans") that are endogenous to the WM-CTRW process. For example, changes of the VAF in the latter case are in the form of some instability and distinctly differ from those caused in the former case. In each case these changes are quite different compared to the situation without super-extreme events suggesting the possibility to detect them in natural system if they occur.
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