随机微分方程的几种参数估计方法（英文）

发布时间：2018-04-11 19:11

本文选题：随机微分方程 + 参数估计　；参考：《中国科学院大学学报》2017年05期

【摘要】：提出3种基于离散观测数据的随机微分方程参数估计的方法。第1种方法应用于线性随机微分方程。推导出这类方程的真解的相关运算服从的分布,使观测数据的运算也服从此分布,由此来估计漂移系数与扩散系数中的未知参数。第2种方法用于Ito^型随机微分方程。推导出Euler-Maruyama格式的数值解的相关运算服从的分布,使观测数据的运算服从此分布,由此来估计参数。第3种方法用于Stratonovich型随机微分方程。推导出中点格式的数值解的相关运算服从的分布,使观测数据的运算服从此分布,以此来估计参数。数值实验验证了这3种方法的有效性。数值实验显示,Euler-Maruyama格式参数估计的误差约为O(h0.5)阶,中点格式参数估计的误差约为O(h)阶,其中h是数值方法的时间步长。我们提出的3种估计方法均比文献中已有的EM-MLE方法更精确。
[Abstract]:Three methods for estimating the parameters of stochastic differential equations based on discrete observation data are presented.The first method is applied to linear stochastic differential equations.The distribution of the dependence of the true solution of the equation is derived, so that the operation of the observed data is applied to the distribution, and the unknown parameters in the drift coefficient and diffusion coefficient are estimated.The second method is applied to Ito ^ type stochastic differential equations.This paper deduces the distribution of the dependent operation clothing of the numerical solution of the Euler-Maruyama scheme, and makes the operation suit of the observation data from this distribution, and then estimates the parameters.The third method is applied to stochastic differential equations of Stratonovich type.In this paper, the distribution of the correlation operation clothing of the numerical solution of the midpoint scheme is derived, and the distribution of the operation suit of the observed data is obtained, so as to estimate the parameters.The effectiveness of these three methods is verified by numerical experiments.Numerical experiments show that the error of parameter estimation in Euler-Maruyama scheme is about 0. 5) order, and the error of parameter estimation in midpoint scheme is about 0. 5) order, where h is the time step of numerical method.The three estimation methods proposed by us are more accurate than the existing EM-MLE methods in the literature.
【作者单位】：中国科学院大学数学科学学院;
【基金】：Supported by the National Natural Science Foundation of China(11471310,11071252)
【分类号】：O211.63

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