A novel exact representation of stationary colored Gaussian processes (fractional differential approach)
A novel exact representation of stationary colored Gaussian processes (fractional differential approach)
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DOI：
10.1088/1751-8113/43/8/085002
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发表时间：
2010-02
期刊：
影响因子：
--
通讯作者：
G. Cottone;M. Paola;R. Santoro
中科院分区：
文献类型：
--
作者：
G. Cottone;M. Paola;R. Santoro
一种新的函数表示，称为广义泰勒形式，被应用于白噪声过程的滤波。证明了每一个高斯彩色噪声都可以表示为一组线性分数阶随机微分方程的输出，其解是分数阶布朗运动的加权和。给出了加权系数的精确形式，并表明它与彩色噪声目标谱密度的分数阶矩有关。
A novel representation of functions, called generalized Taylor form, is applied to the filtering of white noise processes. It is shown that every Gaussian colored noise can be expressed as the output of a set of linear fractional stochastic differential equations whose solution is a weighted sum of fractional Brownian motions. The exact form of the weighting coefficients is given and it is shown that it is related to the fractional moments of the target spectral density of the colored noise.