Cramér Moderate Deviation Expansion for Martingales with One-Sided Sakhanenko’s Condition and Its Applications

Xiequan Fan (), Ion Grama () and Quansheng Liu ()
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Xiequan Fan: Tianjin University
Ion Grama: Univ. Bretagne-Sud
Quansheng Liu: Univ. Bretagne-Sud

Journal of Theoretical Probability, 2020, vol. 33, issue 2, 749-787

Abstract: Abstract 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.

Keywords: Martingales; Cramér moderate deviations; Quantile coupling inequality; $$\beta $$ β -Mixing sequences; $$\psi $$ ψ -Mixing sequences; 60G42; 60F10; 60E15; 60F05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-019-00949-2

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