We consider high-frequency observations from a one-dimensional time-homogeneous diffusion process Y. We assume that the diffusion coefficient $\sigma $ is continuously differentiable in y, but with a jump discontinuity at some level y, say $y=0$. We first study sign-constrained kernel estimators of functions of the left and right limits of $\sigma $ at $0$. These functions intricately depend on both limits. We propose a method to extricate these functions by searching for bandwidths where the kernel estimators are stable by iteration. We finally provide an estimator of the discontinuity jump size. We prove its convergence in probability and discuss its rate of convergence. A Monte Carlo study shows the finite sample properties of this estimator.

我们考虑来自一维时间均匀扩散过程Y的高频观测。我们假设扩散系数$\sigma $在y中连续可微，但在某个级别y处具有跳跃不连续性，例如$y=0$。我们首先研究$\sigma $在$0$左右极限函数的符号约束核估计器。这些功能错综复杂地取决于这两个限制。我们提出了一种通过搜索核估计器通过迭代稳定的带宽来解救这些函数的方法。我们最终提供了不连续跳跃大小的估计器。我们证明了它的概率收敛性并讨论了它的收敛速度。蒙特卡洛研究显示了该估计器的有限样本属性。