标题： 二阶渐近展开用于非同步协变估计量 显示英文标题

标题： Second-order asymptotic expansion for a non-synchronous covariation estimator

摘要： 本文中，我们研究了当观测数据出现非同步性时，估计两种扩散过程协变率的问题。基于近期的论文\cite{Hay-Yos03, Hay-Yos04}，我们在相当一般的设定下（包括随机抽样方案和非预测性随机漂移），推导出了Hayashi-Yoshida估计量分布的二阶渐近展开式。 我们的结果的关键步骤包括：在高斯设定下对估计量分布进行二阶分解，对估计量本身进行随机分解，以及对Malliavin协方差进行精确评估。 为了给出一个具体的例子，我们计算了由两个独立泊松过程生成的抽样方案的特殊情况下的展开式中涉及的常数。 显示英文摘要

摘要： In this paper, we consider the problem of estimating the covariation of two diffusion processes when observations are subject to non-synchronicity. Building on recent papers \cite{Hay-Yos03, Hay-Yos04}, we derive second-order asymptotic expansions for the distribution of the Hayashi-Yoshida estimator in a fairly general setup including random sampling schemes and non-anticipative random drifts. The key steps leading to our results are a second-order decomposition of the estimator's distribution in the Gaussian set-up, a stochastic decomposition of the estimator itself and an accurate evaluation of the Malliavin covariance. To give a concrete example, we compute the constants involved in the resulting expansions for the particular case of sampling scheme generated by two independent Poisson processes.