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Cramér-type moderate deviations for the likelihood ratio process of Ornstein–Uhlenbeck process with shift
Stochastics and Dynamics  (IF0.98),  Pub Date : 2020-09-17, DOI: 10.1142/s0219493721500271
Hui Jiang, Hui Liu

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-$ϕ$ convergence approach, deviation inequalities for multiple Wiener–Itô integrals and asymptotic analysis techniques.