含漂移项分数布朗运动方差估计量的Edgeworth展开

摘要

对含漂移项分数布朗运动方差估计量进行研究.在胡耀忠等人已有工作的基础上,对方差的极大似然估计量的三、四阶原点矩进行计算,并在矩的基础上得到相应的累积量,最后给出标准化后的方差估计量所满足的三项局部Edgeworth展开项.%This article is mainly about the variance estimation for drift fractional brownian motion.Based on maximum likelihood estimator from the work of Hu Yaozhong,etc.,we computed the third and forth moments of the estimator,and also it was cumulants,then we claimed the Edgeworth expansion series for the variance estimation.