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

在流体动力学湍流和非平衡系统的研究中，人们已经证明，所观察到的非高斯概率密度函数往往是有效地描述了高斯分布与波动方差的叠加。基于这个框架，我们提出了一个通用的方法来表征间歇性和非高斯时间序列。在我们的方法中，一个观察到的时间序列被假定为高斯和振幅随机变量的乘积，其中的振幅变量描述的方差波动。分析表明，对数振幅波动的统计特性可以估计使用对数绝对矩的观测时间序列。这种方法适用于各种各样的重尾对称单峰分布。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很宽的非高斯波动范围内提供详细的表征。利用该方法，我们研究了健康人心率变异性，通过粗粒化过程，心率变异性缓慢地收敛到高斯分布;此外，为了研究复杂系统中观察到的不对称间歇波动，我们提出了正或负方向非高斯统计量。作为非对称间歇波动的一个数值例子，我们详细介绍了一个随机级联型模型。使用我们的方法，它表明，心率变异性的不对称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.