Estimation of all parameters in the reflected Ornstein–Uhlenbeck process from discrete observations

Abstract

Assuming that a reflected Ornstein–Uhlenbeck process is observed at discrete time instants, we propose generalized moment estimators to estimate all the drift and diffusion parameters via the celebrated ergodic theorem. With the sampling time step h>0 arbitrarily fixed, we prove the strong consistency and asymptotic normality of our estimators as the sampling size n tends to infinity. This provides a complete solution to an open problem left in Hu et al. (2015).