噪声的随机微分方程模型与应用

Models of Stochastic Differential Equations for Noise and Applications

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。

Stochastic differential equations （SDEs） are investigated to be used to generate samples of the time series of noise. The SDEs is equivalent to a Markov diffusion process. The coefficients of SDE model can be calculated from the relationship between the drift coefficient and the diffusion coefficient and the probability distribution function of the aimed random variables by the aid of the stationary distribution of Markov diffusion processes. A model of the diffusion coefficient as a linear power function is presented. The effects of the different diffusion coefficients on the numerical algorithm of SDEs are discussed. The numerical algorithm of SDEs is outlined, and two different types of numerical algorithm for complex random variables are provided. Finally, taking the Rayleigh distribution and X^2 distribution as examples, this paper verifies the accuracy and effectiveness of the proposed method.