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Cramér Moderate Deviation Expansion for Martingales with One-Sided Sakhanenko’s Condition and Its Applications
Journal of Theoretical Probability ( IF 0.8 ) Pub Date : 2019-10-05 , DOI: 10.1007/s10959-019-00949-2
Xiequan Fan , Ion Grama , Quansheng Liu

We give a Cramér moderate deviation expansion for martingales with differences having finite conditional moments of order $$2+\rho , \rho \in (0,1]$$ 2 + ρ , ρ ∈ ( 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, our result leads to a one-sided moderate deviation principle for martingales. Moreover, applications to quantile coupling inequality, $$\beta $$ β -mixing sequences and $$\psi $$ ψ -mixing sequences are discussed.

中文翻译:

单面Sakhanenko条件鞅的Cramér中度偏差扩展及其应用

我们为鞅给出了一个 Cramér 中等偏差展开式,其差分具有有限条件矩 $$2+\rho , \rho \in (0,1]$$ 2 + ρ , ρ ∈ ( 0 , 1 ] , 和有限一-边条件指数矩。有效范围的上限和我们扩展的剩余部分都是最优的。因此,我们的结果导致了鞅的单边适度偏差原则。此外,应用于分位数耦合不等式,$$\讨论了 beta $$ β-混合序列和 $$\psi $$ ψ-混合序列。
更新日期:2019-10-05
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