This paper deals with the problem of outliers in high frequency observation data from diffusion processes. Robust estimation methods are needed because the inclusion of outliers can lead to incorrect statistical inference even in the diffusion process. To construct a robust estimator, we first approximate the transition density of the diffusion process to the Gaussian density by using Kessler's approach and then employ two types of minimum robust divergence estimation methods. In this paper, we provide the asymptotic properties of the robust estimator using $γ$-divergence. Furthermore, we derive the conditional influence functions of the estimation using divergences and discuss its boundness.

翻译：本文针对扩散过程高频观测数据中的异常值问题展开研究。由于异常值的引入可能导致扩散过程统计推断的偏差，因此需要采用稳健估计方法。为构建稳健估计量，我们首先采用Kessler方法将扩散过程的转移密度近似为高斯密度，继而运用两类最小稳健散度估计方法。本文给出了基于γ-散度的稳健估计量的渐近性质，并推导了散度估计的条件影响函数，同时讨论了其有界性。