协方差或相关的非平稳高斯或代数涨落的多元振幅精确分布
Exact Multivariate Amplitude Distributions for Non-Stationary Gaussian or Algebraic Fluctuations of Covariances or Correlations
摘要：
复杂系统往往是非平稳的，典型的指标是统计特性连续变化的时间序列。特别是，不同时间序列之间的相关性波动。描述这种系统的多变量振幅分布的模型是相当感兴趣的。扩展以前的工作，我们认为一组测量，非平稳相关矩阵作为一个合奏，我们建立了一个随机矩阵模型。我们使用这个合奏平均平稳的多变量振幅分布测量短的时间尺度，从而获得大的时间尺度的多变量振幅分布的特征重尾。我们明确地工作了四种情况下，结合高斯分布和代数分布。所得结果要么是封闭形式，要么是单积分形式。因此，我们提供，第一，明确的多元分布，这样的非平稳系统，第二，一个工具，定量捕获的相关性的非平稳程度。
英文摘要：
Complex systems are often non-stationary, typical indicators are continuously changing statistical properties of time series. In particular, the correlations between different time series fluctuate. Models that describe the multivariate amplitude distributions of such systems are of considerable interest. Extending previous work, we view a set of measured, non-stationary correlation matrices as an ensemble for which we set up a random matrix model. We use this ensemble to average the stationary multivariate amplitude distributions measured on short time scales and thus obtain for large time scales multivariate amplitude distributions which feature heavy tails. We explicitly work out four cases, combining Gaussian and algebraic distributions. The results are either of closed forms or single integrals. We thus provide, first, explicit multivariate distributions for such non-stationary systems and, second, a tool that quantitatively captures the degree of non-stationarity in the correlations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
