Parameter estimation for the drift of a time-inhomogeneous jump diffusion process

Abstract

This work deals with parameter estimation for the drift of jump diffusion processes which are driven by a Lévy process and whose drift term is linear in the parameter. In contrast to the commonly used maximum likelihood estimator, our proposed estimator has the practical advantage that its calculation does not require the evaluation of the continuous part of the sample path. In the important case of an Ornstein-Uhlenbeck-type jump diffusion, which is a widely used model, we prove consistency of our estimator.