Sequential maximum likelihood estimation for reflected generalized Ornstein–Uhlenbeck processes

Abstract

In this paper, we investigate a sequential maximum likelihood estimator of the unknown drift parameter for a class of reflected generalized Ornstein–Uhlenbeck processes driven by spectrally positive Lévy processes. In both of the cases of negative drift and positive drift, we prove that the sequential maximum likelihood estimator of the drift parameter is closed, unbiased, normally distributed and strongly consistent. Finally a numerical test is presented to illustrate the efficiency of the estimator.