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.

中文翻译：

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Ornstein-Uhlenbeck 过程的似然比过程的 Cramér 型中度偏差

对于静止和爆炸情况下的Ornstein-Uhlenbeck过程，本文研究了对数似然比过程的Cramér型中度偏差。作为一个应用程序，我们给出了漂移测试问题的负区域，并获得了错误概率的衰减率。本文的主要方法包括 mod-[公式：见正文] 收敛方法、多重 Wiener-Itô 积分的偏差不等式和渐近分析技术。