Average shape of a fluctuation: Universality in excursions of stochastic processes
Average shape of a fluctuation: Universality in excursions of stochastic processes
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DOI：
10.1103/physrevlett.90.060601
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发表时间：
2003-02-14
影响因子：
8.6
通讯作者：
Castellano, C
中科院分区：
文献类型：
--
作者：
Baldassarri, A;Colaiori, F;Castellano, C
我们研究时间序列x（t）的波动的平均形状，它是x（t）在时间T首次返回到其初始值x（0）之前的平均值[x（t）- x（0）]（T）。对于大类随机过程，我们发现服从形式为[x（t）- x（0）]（T）= T（α）f（t/T）的标度律.尺度函数f（s）在很大程度上独立于单个增量分布的细节，而它编码了关于过程中时间相关性的存在和性质的相关统计信息。我们讨论的相关性，这些结果的巴克豪森噪声在磁系统。
We study the average shape of a fluctuation of a time series x(t), which is the average value [x(t) - x(0)](T) before x(t) first returns at time T to its initial value x(0). For large classes of stochastic processes, we find that a scaling law of the form [x(t) - x(0)](T) = T(alpha)f(t/T) is obeyed. The scaling function f(s) is, to a large extent, independent of the details of the single increment distribution, while it encodes relevant statistical information on the presence and nature of temporal correlations in the process. We discuss the relevance of these results for Barkhausen noise in magnetic systems.