弱相关事件间时间的解析可解自相关函数
Analytically solvable autocorrelation function for weakly correlated interevent times
摘要：
在自然和社会现象的事件序列中观察到的长期时间相关性的特征在于代数衰减的自相关函数。这样的时间相关性不仅可以通过异质间隔时间（Iths）来理解，而且可以通过Iths之间的相关性来理解。与异质性Ikr对自相关函数的作用相反，由于Ikr之间的相关性，对Ikr的影响知之甚少。为了严格地研究这些影响，我们推导出任意IET分布的自相关函数的解析形式的情况下，弱相关的IET，其中的Farlie-Gumbel-Morgenstern copula是采用建模的联合概率分布函数的两个连续的IET。我们的分析结果证实了指数和幂律IET分布的数值模拟。对于幂律的情况下，我们发现的自相关函数的陡峭的衰减的趋势，Iklv之间的较强的相关性。我们的分析方法，使我们能够更好地了解长期的时间相关性引起的Icons之间的相关性。
英文摘要：
Long-term temporal correlations observed in event sequences of natural and social phenomena have been characterized by algebraically decaying autocorrelation functions. Such temporal correlations can be understood not only by heterogeneous interevent times (IETs) but also by correlations between IETs. In contrast to the role of heterogeneous IETs on the autocorrelation function, yet little is known about the effects due to the correlations between IETs. In order to rigorously study these effects, we derive an analytical form of the autocorrelation function for the arbitrary IET distribution in the case with weakly correlated IETs, where the Farlie-Gumbel-Morgenstern copula is adopted for modeling the joint probability distribution function of two consecutive IETs. Our analytical results are confirmed by numerical simulations for exponential and power-law IET distributions. For the power-law case, we find a tendency of the steeper decay of the autocorrelation function for the stronger correlation between IETs. Our analytical approach enables us to better understand long-term temporal correlations induced by the correlations between IETs.
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