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Article Dans Une Revue Journal of Theoretical Probability Année : 2019

Cram\'{e}r moderate deviation expansion for martingales with one-sided Sakhanenko's condition and its applications

Résumé

We give a Cram\'{e}r moderate deviation expansion for martingales with differences having finite conditional moments of order $2+\rho, \rho \in (0,1],$ and finite one-sided conditional exponential moments. The upper bound of the range of validity and the remainder of our expansion are both optimal. Consequently, it leads to a "half-side" moderate deviation principle for martingales. It is worth mentioning that our result is new even for independent random variables. Moreover, applications to quantile coupling inequality, $\beta$-mixing and $\psi$-mixing sequences are discussed.
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hal-02487919 , version 1 (21-02-2020)

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Xiequan Fan, Ion Grama, Quansheng Liu. Cram\'{e}r moderate deviation expansion for martingales with one-sided Sakhanenko's condition and its applications. Journal of Theoretical Probability, In press. ⟨hal-02487919⟩
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