Vahabi M, Jafari G R
School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Dec;86(6 Pt 2):066704. doi: 10.1103/PhysRevE.86.066704. Epub 2012 Dec 17.
In this paper, we introduce a simple and practical method to generate Gaussian self-similar stochastic processes [fractional Gaussian noises (fGns) and fractional Brownian motions (fBms)] by interpolating between two known series of them. We apply the rotation algorithm to different cases including different pairs of fBms (fGns) and also different pairs each composed of an fBm and an fGn. Our results show that the sensitivity of our method for two fBms (fGns) is higher when approaching the series with a larger (smaller) Hurst exponent and, for the case with one fBm and one fGn by approaching the Hurst exponent of the selected fBm, the Hurst exponent of the produced series changes more. Surprisingly, by using this method, we can generate (positively and/or negatively) correlated series from two uncorrelated ones (one Brownian motion and one white Gaussian noise) or it is possible to generate uncorrelated signals (one or two depending on the choice of two input signals) from two correlated ones. For two fGns, using the rotation algorithm, the evolution starts from larger scales in the system, while for two fBms, the evolution starts from smaller scales in the system.
在本文中，我们介绍了一种简单实用的方法，通过在两个已知的高斯自相似随机过程（分数高斯噪声（fGn）和分数布朗运动（fBm））序列之间进行插值来生成它们。我们将旋转算法应用于不同的情况，包括不同的fBm（fGn）对，以及由一个fBm和一个fGn组成的不同对。我们的结果表明，当接近具有较大（较小）赫斯特指数的序列时，我们的方法对两个fBm（fGn）的敏感性更高；对于一个fBm和一个fGn的情况，通过接近所选fBm的赫斯特指数，生成序列的赫斯特指数变化更大。令人惊讶的是，使用这种方法，我们可以从两个不相关的序列（一个布朗运动和一个白高斯噪声）生成（正和/或负）相关序列，或者有可能从两个相关序列生成不相关信号（一个或两个，取决于两个输入信号的选择）。对于两个fGn，使用旋转算法时，系统中的演化从较大尺度开始，而对于两个fBm，演化从系统中的较小尺度开始。
