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arXiv · 1909.05112

Cramér moderate deviation expansion for martingales with one-sided Sakhanenko's condition and its applications

Xiequan Fan·Ion Grama·Quansheng Liu
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Abstract

We give a Cramér moderate deviation expansion for martingales with differences having finite conditional moments of order $2+ρ, ρ\in (0,1],$ 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, $β$-mixing and $ψ$-mixing sequences are discussed.

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Xiequan Fan, Ion Grama, Quansheng Liu. 2019-09-12. Cramér moderate deviation expansion for martingales with one-sided Sakhanenko's condition and its applications. https://doi.org/10.1007/s10959-019-00949-2

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