Nonparametric Estimation of a Diffusion Equation from Tick Observations
We propose a nonparametric estimation technique of the coefficients of an univariate diffusion process. The estimation is done with a process observed at random times, corresponding to the crossing times of discrete levels. We first estimate the scale function of the process, which allows to transform any diffusion into a local martingale. This function is independent of the set of observation dates of the continuous time process.