Cramér-type moderate deviations for the likelihood ratio process of Ornstein–Uhlenbeck process with shift

Abstract

For the Ornstein–Uhlenbeck process in stationary and explosive cases, this paper studies Cramér-type moderate deviations for the log-likelihood ratio process. As an application, we give the negative regions of drift testing problem, and also obtain the decay rates of the error probabilities. The main methods of this paper consist of mod-[Formula: see text] convergence approach, deviation inequalities for multiple Wiener–Itô integrals and asymptotic analysis techniques.