相关时间序列中罕见事件重现期的分布
Distribution of Return Periods of Rare Events in Correlated Time Series
摘要：
我们研究了非指数衰减的有限项相关性时间序列中罕见事件的重现期分布的影响。精确地说，我们分析了非平衡稳态下颗粒结构电阻的自关联函数和电阻涨落极值返回区间的统计特性。电阻波动，$δR$，通过蒙特卡罗模拟计算，使用SBRN模型介绍了几年前由Pennetta，Trefán和Reggiani和基于电阻网络的方法。当$δR$超过显著高于电阻平均值的阈值$q$时，发生罕见事件。我们已经发现，对于高度无序的网络，当自关联函数显示非指数衰减但电阻波动的特征在于有限的相关时间时，极值的返回间隔的分布由拉伸指数很好地描述，指数在很大程度上与阈值$q$无关。我们讨论了这一结果和一些主要的未决问题，它与其他作者最近的研究结果有关的观察拉伸指数分布的极端事件的返回间隔在长期相关的时间序列。
英文摘要：
We study the effect on the distribution of return periods of rare events of the presence in a time series of finite-term correlations with non-exponential decay. Precisely, we analyze the auto-correlation function and the statistics of the return intervals of extreme values of the resistance fluctuations displayed by a resistor with granular structure in a nonequilibrium stationary state. The resistance fluctuations, $δR$, are calculated by Monte Carlo simulations using the SBRN model introduced some years ago by Pennetta, Trefán and Reggiani and based on a resistor network approach. A rare event occurs when $δR$ overcomes a threshold value $q$ significantly higher than the average value of the resistance. We have found that for highly disordered networks, when the auto-correlation function displays a non-exponential decay but yet the resistance fluctuations are characterized by a finite correlation time, the distribution of return intervals of the extreme values is well described by a stretched exponential, with exponent largely independent of the threshold $q$. We discuss this result and some of the main open questions related to it, also in connection with very recent findings by other authors concerning the observation of stretched exponential distributions of return intervals of extreme events in long-term correlated time series.
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