一种随机微分方程中布朗运动的方差估计

A Variance Estimation of Brownian Motion in Stochastic Differential Equations

随机微分方程已在各个领域广泛应用,其参数估计问题是该领域重要的研究内容之一.利用抽样数据给出了一类随机微分方程中布朗运动的方差估计方法,通过离散方法给出由抽样数据构成方差估算的表达式.实例模拟分析表明:采样区间长度越小,该方法估算的方差误差越小.说明该方法是可行的,具有很好的实际应用价值.

Stochastic differential equations have been widely used in various fields,and its parameter estimation problem is one of the important research contents in this field. In this paper,the estimation method of the variance of the Brownian motion in a class of stochastic differential equations is given by using the sampled data. The expression of the variance estimation from the sampled data is given by the discrete method. The simulation analysis shows that the smaller the sampling interval length is,the smaller the variance error estimated by this method is. It shows that the method is feasible and has certain practical value.