On the number of crossings and bouncings of a diffusion at a sticky threshold
Résumé
We distinguish between three types of crossing of a sticky threshold by a onedimensional diffusion. We examine the limit behavior of the corresponding number of crossings statistics and prove that each of these statistics has a different asymptotic regime. We define the notions of bouncing as the symmetric counterparts of crossings. We prove similar results for the number of bouncings at reflecting and non-reflecting sticky thresholds. Using these, we develop consistent stickiness parameter estimators for sticky diffusions and sticky-reflecting Brownian motion.
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