HOW LARGE IS THE JUMP DISCONTINUITY IN THE DIFFUSION COEFFICIENT OF A TIME-HOMOGENEOUS DIFFUSION?
针对一维时间齐次扩散过程，假设扩散系数在某个水平处存在跳跃不连续，提出一种通过迭代搜索稳定带宽来估计跳跃大小的方法，并证明其收敛性。
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.