连续随机变量非线性函数的概率密度函数研究

发布时间：2018-04-29 18:07

本文选题：连续随机变量 + 非线性　；参考：《科技通报》2017年08期

【摘要】：概率密度函数对系统的随机性能有更为全面的描述,因此文中将连续随机变量非线性函数的概率密度函数作为研究对象,提出一种引入辅助随机变量求解非线性密度函数的方法。首先,针对随机变量的密度函数,利用概率密度演化方法,通过引入时间变量使问题转换为关于联合概率密度的偏微分方程,获取边缘密度得到函数的解析解,而对于部分密度函数的广义函数,则需引入辅助随机变量对函数进行数值积分后通过傅里叶变换获取概率密度;其次,对于非线性系统的概率密度函数,提出基于非线性系统的状态变量子空间法,在任意一子空间上对FPK方程进行积分获取低维的FPK方程,通过等效线性化处理达到表述非线性概率密度函数的目的。实验证明,通过对非线性概率密度函数的有效研究可为非线性系统控制提供可靠的理论基础。
[Abstract]:The probability density function has a more comprehensive description of the stochastic performance of the system, so the probability density function of the nonlinear function of the continuous random variable is regarded as the research object in this paper. A method for solving nonlinear density function with auxiliary random variables is proposed. Firstly, according to the density function of random variables, using the method of probability density evolution, the problem is transformed into partial differential equation about joint probability density by introducing time variable, and the analytic solution of the function is obtained by edge density. For the generalized function of partial density function, it is necessary to introduce auxiliary random variables to the function and obtain the probability density by Fourier transform. Secondly, for the probability density function of nonlinear system, A state variable subspace method based on nonlinear systems is proposed to obtain the low-dimensional FPK equation by integrating the FPK equation on any subspace. The nonlinear probability density function can be expressed by equivalent linearization. The experimental results show that the effective study of nonlinear probability density function can provide a reliable theoretical basis for nonlinear system control.
【作者单位】：集宁师范学院数学系;
【基金】：国家自然科学基金青年科学基金(61503269)
【分类号】：O211

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