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We study the Nadaraya-Watson (N-W) estimator for the drift function oftwo-sided reflected stochastic processes. We propose a discrete-type N-Westimator and a continuous-type N-W estimator based on the discretely observedprocesses and continuously observed processes respectively. Under some regularconditions, we obtain the consistency and give the asymptotic distributions forthe two estimators. Furthermore, we briefly remark that our method can beapplied to the one-sided reflected stochastic processes spontaneously.Numerical studies show that the proposed estimators is adequate for practicaluse.

Nadaraya-Watson estimator for reflected stochastic processes driven by Brownian motions