Statistical mechanism of intermittent fluctuations observed in nonlinear nonequilibrium system and its applications

在流体动力湍流和非平衡系统的研究中，已经证明观测到的非高斯概率密度函数通常可以通过具有波动方差的高斯分布的叠加来有效地描述。基于这个框架，我们提出了一种表征间歇和非高斯时间序列的通用方法。在我们的方法中，假设观察到的时间序列由高斯和振幅随机变量的乘法来描述，其中振幅变量描述方差波动。分析表明，对数振幅波动的统计性质可以用观测到的时间序列的对数绝对矩估计。该方法适用于各种重尾对称单峰分布。通过分析随机级联型过程和超统计非高斯模型，我们证明了我们的方法可以在大范围的非高斯波动中提供详细的表征。利用该方法，我们研究了健康心率变异性，该变异性通过粗粒度处理缓慢收敛到高斯分布。此外，为了研究复杂系统中观察到的不对称间歇性波动，我们提出了正方向或负方向非高斯统计量。作为不对称间歇波动的数值例子，我们启发式地引入了一个随机级联型模型。使用我们的方法，证明心率变异性的不对称特性取决于年龄和自主神经紊乱。

In studies of hydrodynamic turbulence and nonequilibrium systems, it has been demonstrated that the observed non-Gaussian probability density functions are often described effectively by a superposition of Gaussian distributions with fluctuating variances. Based on this framework, we propose a general method to characterize intermittent and non-Gaussian time series. In our approach, an observed time series is assumed to be described by the multiplication of Gaussian and amplitude random variables, where the amplitude variable describes the variance fluctuation. It is shown analytically that statistical properties of the log-amplitude fluctuations can be estimated using the logarithmic absolute moments of the observed time series. This method is applicable to a wide variety of symmetric unimodal distributions with heavy tails. By analyzing random cascade-type processes and superstatistical non-Gaussian models, we demonstrate that our method can provide detailed characterization in a wide range of non-Gaussian fluctuations. Using this method, we study healthy heart rate variability, which show the slow convergence to a Gaussian distribution through coarse graining procedure.Moreover, to study asymmetric intermittent fluctuations observed in complex systems, we propose positive- or negative-directional non-Gaussian statistics. As a numerical example of asymmetric intermittent fluctuations, we heuristically introduce a random cascade-type model. Using our method, it is demonstrated that the asymmetric properties of heart rate variability depend on aging and autonomic disorder.