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Cram\'{e}r moderate deviation expansion for martingales with one-sided Sakhanenko's condition and its applications
- Source :
- Journal of Theoretical Probability (2020)
- Publication Year :
- 2019
-
Abstract
- 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.<br />Comment: 24 pages
- Subjects :
- Mathematics - Probability
60G42, 60F10, 60E15, 60F05
Subjects
Details
- Database :
- arXiv
- Journal :
- Journal of Theoretical Probability (2020)
- Publication Type :
- Report
- Accession number :
- edsarx.1909.05112
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s10959-019-00949-2