Title: Statistical estimation of the Oscillating Brownian Motion,
Abstract: We study the asymptotic behavior of estimators of a two-valued, discontinuous
diffusion coefficient in a Stochastic Differential Equation, called an
Oscillating Brownian Motion. Using the relation of the latter process with the
Skew Brownian Motion, we propose two natural consistent estimators, which are
variants of the integrated volatility estimator and take the occupation times
into account. We show the stable convergence of the renormalized errors'
estimations toward some Gaussian mixture, possibly corrected by a term that
depends on the local time. These limits stem from the lack of ergodicity as
well as the behavior of the local time at zero of the process. We test both
estimators on simulated processes, finding a complete agreement with the
theoretical predictions.