非同步协变估计量的二阶渐近展开
Second-order asymptotic expansion for a non-synchronous covariation estimator
摘要：
本文考虑了观测值具有非同步性时两个扩散过程协变的估计问题。在最近的论文\cite{Hay-Yos03, Hay-Yos04}的基础上，我们推导了在随机抽样方案和非预期随机漂移的相当一般的设置中的Hayashi-Yoshida估计的分布的二阶渐近展开。导致我们的结果的关键步骤是二阶分解的估计的分布在高斯设置，估计本身的随机分解和准确的评估Malliavin协方差。为了给出一个具体的例子，我们计算的常数所产生的扩展的特殊情况下的抽样方案产生的两个独立的泊松过程。
英文摘要：
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.
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