Systems with correlations in the variance: Generating power law tails in probability distributions
Systems with correlations in the variance: Generating power law tails in probability distributions
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DOI：
10.1209/epl/i2000-00540-7
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发表时间：
1999-10
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影响因子：
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通讯作者：
Boris Podobnik;P. Ivanov;Youngki Lee;Alessandro Chessa;H. Stanley
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文献类型：
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作者：
Boris Podobnik;P. Ivanov;Youngki Lee;Alessandro Chessa;H. Stanley
我们研究如何在物理变量的相关性的存在有助于概率分布的形式。我们研究了一个方差相关的过程，该过程由i）高斯分布或ii）截断的Lévy分布产生。对于i）和ii），我们发现由于方差的相关性，该过程“动态地”在分布中产生幂律尾，其指数可以通过引入方差的相关性的方式来控制。对于ii），我们发现该过程可以将截断分布扩展到截断截止之外，这导致Lévy稳定幂律与当前“动态生成”幂律之间的交叉。我们发现，该过程可以解释最近观察到的交叉行为在标准普尔500指数。
We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by i) a Gaussian or ii) a truncated Lévy distribution. For both i) and ii), we find that due to the correlations in the variance, the process “dynamically” generates power law tails in the distributions, whose exponents can be controlled through the way the correlations in the variance are introduced. For ii), we find that the process can extend a truncated distribution beyond the truncation cutoff, which leads to a crossover between a Lévy stable power law and the present “dynamically generated” power law. We show that the process can explain the crossover behavior recently observed in the S&P500 stock index.