Automatic algorithm to decompose discrete paths of fractional Brownian motion into self-similar intrinsic components
Automatic algorithm to decompose discrete paths of fractional Brownian motion into self-similar intrinsic components
复制标题
将分数布朗运动的离散路径分解为自相似内在分量的自动算法
DOI：
10.1140/epjb/e2015-60515-5
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
N. Suciu
中科院分区：
文献类型：
--
作者：
Vamoş;M. Crăciun;N. Suciu
分数布朗运动(FBM)是一种非平稳的自相似连续随机过程，用于模拟许多自然现象。FBM的实现可以由不完全保持自相似性的离散路径来数值逼近。我们通过将FBM的离散路径分解为本征分量来研究不同时间尺度下的自相似性。分解由一种基于逐次平滑的自动数值算法实现，该算法在平均时间序列达到最大单调方差时停止。通过定义为单调段的幅度相对于其长度(特征时间)的图的单调谱来分析本征分量的谱特性。结果表明，在中间时间尺度上，离散FBM的本征分量的平均幅值与相应的连续FBM的平均特征时间成幂函数关系。作为应用，我们考虑随机速度场中扩散运动与平流输送的叠加所产生的输送过程横向分量的水文时间序列。我们发现，横向分量具有丰富的尺度结构，这是全局方差分析所不能揭示的，而且其固有分量只有在特定情况下才可能是自相似的。
Fractional Brownian motion (fBm) is a nonstationary self-similar continuous stochastic process used to model many natural phenomena. A realization of the fBm can be numerically approximated by discrete paths which do not entirely preserve the self-similarity. We investigate the self-similarity at different time scales by decomposing the discrete paths of fBm into intrinsic components. The decomposition is realized by an automatic numerical algorithm based on successive smoothings stopped when the maximum monotonic variation of the averaged time series is reached. The spectral properties of the intrinsic components are analyzed through the monotony spectrum defined as the graph of the amplitudes of the monotonic segments with respect to their lengths (characteristic times). We show that, at intermediate time scales, the mean amplitude of the intrinsic components of discrete fBms scales with the mean characteristic time as a power law identical to that of the corresponding continuous fBm. As an application we consider hydrological time series of the transverse component of the transport process generated as a superposition of diffusive movements on advective transport in random velocity fields. We found that the transverse component has a rich structure of scales, which is not revealed by the analysis of the global variance, and that its intrinsic components may be self-similar only in particular cases.
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DOI：
10.1140/epjb/e2014-50596-y
发表时间：
2014
期刊：
The European Physical Journal B
影响因子：
--
作者：
C. Vamos;M. Craciun
通讯作者：
M. Craciun
影响因子：
2.4
作者：
Carbone, A;Castelli, G;Stanley, HE
通讯作者：
Stanley, HE
去趋势时间序列的序列相关性。
DOI：
10.1103/physreve.78.036707
发表时间：
2008
期刊：
Physical review. E, Statistical, nonlinear, and soft matter physics
影响因子：
--
作者：
C. Vamos;M. Craciun
通讯作者：
M. Craciun
DOI：
10.1098/rspa.1998.0193
发表时间：
1998-03-08
影响因子：
3.5
作者：
Huang, NE;Shen, Z;Liu, HH
通讯作者：
Liu, HH
空间不均匀转移概率作为统计均匀随机速度场中扩散的记忆效应。
DOI：
10.1103/physreve.81.056301
发表时间：
2010
期刊：
Physical review. E, Statistical, nonlinear, and soft matter physics
影响因子：
--
作者：
N. Suciu
通讯作者：
N. Suciu