Functional convergence to the local time of a sticky diffusion

Abstract

We prove the consistency of a local time approximation of a sticky diffusion, based on high-frequency observation of the underlying process. First, we prove this for the sticky Brownian motion. Then, extend the result to Itô diffusions with a sticky point (SID). For this, we prove the path-wise formulation of an SID. We then devise a consistent estimator of the stickiness parameter built upon the local time approximation. Last, we perform numerical experiments to assess the statistical properties of the stickiness estimator and the local time approximation.