Cramér-type moderate deviations for the log-likelihood ratio of inhomogeneous Ornstein–Uhlenbeck processes

Abstract

We consider the Cramér-type moderate deviations for the log-likelihood ratio of the inhomogeneous Ornstein–Uhlenbeck processes in the stationary and explosive cases. The relative error of tail probability of the log-likelihood ratio is quantified by deviation inequalities for multiple Wiener–Itô integrals and mod-ϕ convergence approach. As the special cases, we get the Cramér-type moderate deviations of the Ornstein–Uhlenbeck process and α-Wiener bridge.