Cram?r-type moderate deviations for the log-likelihood ratio of inhomogeneous Ornstein-Uhlenbeck processes

Authors：Cui, Jiazhen; Liu, Qiaojing^*

Source：STATISTICS & PROBABILITY LETTERS, 2023, 192: 109690.

DOI：10.1016/j.spl.2022.109690

• Log-likelihood ratio
• Cram?r moderate deviations
• Ornstein-Uhlenbeck process
• ?-Wiener bridge

We consider the Cramer-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-Ito integrals and mod-phi convergence approach. As the special cases, we get the Cramer-type moderate deviations of the Ornstein-Uhlenbeck process and alpha-Wiener bridge.