Nonergodicity of a time series obeying Levy statistics
Nonergodicity of a time series obeying Levy statistics
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DOI：
10.1007/s10955-005-8076-9
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发表时间：
2006-01-01
影响因子：
1.6
通讯作者：
Barkai, E
中科院分区：
文献类型：
--
作者：
Margolin, G;Barkai, E
研究了在 1 和 0 之间切换并受宽幂律停留时间分布控制的二分随机过程的时间平均自相关函数。这种称为 Levy walk 的过程描述了许多物理系统的动态行为，连续激光照射下半导体纳米晶体的荧光间歇就是一个例子。当平均停留时间出现偏差时，该过程是非遍历的。适合这种情况，时间平均自相关函数不等于集合平均自相关函数，而是即使在长测量时间的限制下也保持随机性。对于不同的参数范围，获得了该随机自相关函数的分布的几种近似值，并且与蒙特卡罗模拟相比具有优势。简要讨论了过程功率谱的非遍历性，并提出了将相关函数与功率谱联系起来的非平稳维纳辛钦定理。所考虑的情况与遍历性和平稳性的通常假设完全相反。
Time-averaged autocorrelation functions of a dichotomous random process switching between 1 and 0 and governed by wide power law sojourn time distribution are studied. Such it process, called a Levy walk, describes dynamical behaviors of many physical systems, fluorescence intermittency of semiconductor nanocrystals under Continuous laser illumination being one example. When the mean sojourn time diverges the process is non-ergodic. fit that case, the time average autocorrelation function is not equal to the ensemble averaged autocorrelation function, instead it remains random even in the limit of long measurement time. Several approximations for the distribution Of this random autocorrelation function are obtained for different parameter ranges, and favorably compared to Monte Carlo simulations. Nonergodicity of the power spectrum of the process is briefly discussed, and a nonstationary Wiener-Khintchine theorem, relating the correlation functions and the power spectrum is presented. The considered situation is in full contrast to the Usual assumptions of ergodicity and stationarity.