📝 SummarXiv

Abstract

We study a class of high-frequency path functionals for diffusions with singular thresholds or boundaries, where the process exhibits either (i) skweness, oscillating coefficients, and stickiness, or (ii) sticky reflection. The functionals are constructed from a test function and a diverging normalizing sequence. We establish convergence to local time, generalizing existing results for these processes. Notably, our framework allows for any normalizing sequence diverging slower than the observation frequency and for thresholds that are jointly skew-oscillating-sticky (thresholds where stickiness, oscillations, and skewness occur). Combining our results with occupation time approximations, we develop consistent estimators for stickiness and skewness parameters at thresholds that exhibit any combination of these features (stickiness, oscillation, skewness, and reflection).