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We prove the convergence of a class of high frequency path-functionals of asticky diffusion to its local time. First, we prove this for the stickyBrownian motion. Then, we extend the result to sticky stochastic differentialequations. We combine the local time approximation with an approximation of theoccupation time to set up a consistent stickiness estimator. Last, we performnumerical experiments to assess the properties of the stickiness estimator andthe local time approximation.

Functional convergence to the local time of sticky diffusions