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

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  • Cui, Jiazhen
  • Liu, Qiaojing

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.

Suggested Citation

  • Cui, Jiazhen & Liu, Qiaojing, 2023. "Cramér-type moderate deviations for the log-likelihood ratio of inhomogeneous Ornstein–Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:stapro:v:192:y:2023:i:c:s0167715222002036
    DOI: 10.1016/j.spl.2022.109690
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    References listed on IDEAS

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    1. Zhao, Shoujiang & Zhou, Qianqian, 2019. "On large deviation expansion for log-likelihood ratio of non-homogeneous Ornstein–Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    2. Fan, Xiequan & Grama, Ion & Liu, Quansheng & Shao, Qi-Man, 2020. "Self-normalized Cramér type moderate deviations for stationary sequences and applications," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 5124-5148.
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