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研究使用随机微分方程(SDEs)产生各种噪声的时间序列样本,该SDEs等效于一个Mark-ov扩散过程。由Markov扩散过程的平稳分布可以得到SDEs模型中漂移系数和扩散系数与待求噪声所满足的概率密度函数之间的解析关系,从而可以确定SDEs模型中的系数。给出了一种线性幂函数的扩散系数模型,讨论了此种类型的扩散系数对SDEs数值算法的影响。给出了SDEs模型的数值算法,并针对复杂随机变量提出了两种不同的SDEs模型生成方法。以Rayleigh分布和χ2分布为例进行仿真分析,验证本文所提方法的准确性和有效性。
We study time-series samples of various noises using stochastic differential equations (SDEs), which is equivalent to a Markov-ov diffusion process. The stable distribution of Markov diffusion process can get the analytic relationship between the drift coefficient and diffusion coefficient in SDEs model and the probability density function satisfied by the noise to be sought, so that the coefficients in the SDEs model can be determined. A diffusion coefficient model of linear power function is given. The influence of diffusion coefficient of this type on the numerical algorithm of SDEs is discussed. The numerical algorithm of SDEs model is given, and two different SDEs model generation methods are proposed for complex random variables. The Rayleigh distribution and χ2 distribution are taken as an example to verify the accuracy and effectiveness of the proposed method.