HOW LARGE IS THE JUMP DISCONTINUITY IN THE DIFFUSION COEFFICIENT OF A TIME-HOMOGENEOUS DIFFUSION?
时齐扩散过程的扩散系数跳跃有多大？
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…