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摘要翻译：
研究了从初值测得最大值时时间信号的极值统计量。在独立同分布(iid)变量的情况下，根据引出变量的父分布的性质，对最大值的极限分布进行了分类。然后我们转向具有1/f^α功率谱的相关周期高斯信号，研究了最大相对高度相对于初始高度(MRH_I)的分布。导出了Alpha=0(iid变量）,Alpha=2（随机游动）,Alpha=4（随机加速）,Alpha=无穷大（单正弦模式）的精确MRH_I分布。对于α的其他中间值，分布由模拟确定。我们发现MRH_I分布明显不同于以前研究的所有α的最大高度相对于平均高度的分布。MRH_I分布的两个主要特征是相对高度较小时权重较大，α>3时零高度发散。我们还通过对一些非周期边界条件的精确结果证明了边界条件对分布形状的影响。最后，我们证明了对于来自时间平移不变分布的信号，其近极端态密度与MRH_I分布相同。这被用来发展两个分布的阈值奇点的标度理论。
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英文标题：
《Extreme statistics for time series: Distribution of the maximum relative
to the initial value》
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作者：
T. W. Burkhardt (Temple University), G. Gyorgyi, N. R. Moloney, Z.
Racz (Eotvos University)
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
The extreme statistics of time signals is studied when the maximum is measured from the initial value. In the case of independent, identically distributed (iid) variables, we classify the limiting distribution of the maximum according to the properties of the parent distribution from which the variables are drawn. Then we turn to correlated periodic Gaussian signals with a 1/f^alpha power spectrum and study the distribution of the maximum relative height with respect to the initial height (MRH_I). The exact MRH_I distribution is derived for alpha=0 (iid variables), alpha=2 (random walk), alpha=4 (random acceleration), and alpha=infinity (single sinusoidal mode). For other, intermediate values of alpha, the distribution is determined from simulations. We find that the MRH_I distribution is markedly different from the previously studied distribution of the maximum height relative to the average height for all alpha. The two main distinguishing features of the MRH_I distribution are the much larger weight for small relative heights and the divergence at zero height for alpha>3. We also demonstrate that the boundary conditions affect the shape of the distribution by presenting exact results for some non-periodic boundary conditions. Finally, we show that, for signals arising from time-translationally invariant distributions, the density of near extreme states is the same as the MRH_I distribution. This is used in developing a scaling theory for the threshold singularities of the two distributions.
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PDF链接：
https://arxiv.org/pdf/707.2753
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