Cramer large deviation expansions for martingales under Bernstein's condition

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Fan, Xiequan¹  Grama, Ion¹  Liu, Quansheng¹ 

[1] Univ Bretagne Sud, LMBA, UMR CNRS 6205, F-56017 Vannes, France

关键词: Expansions of large deviations;    Cramer type large deviations;    Large deviations;    Moderate deviations;    Exponential inequality;    Bernstein's condition;    Central limit theorem;   

DOI  :  10.1016/j.spa.2013.06.010

来源: Elsevier

【 摘 要 】

An expansion of large deviation probabilities for martingales is given, which extends the classical result due to Cramer to the case of martingale differences satisfying the conditional Bernstein condition. The upper bound of the range of validity and the remainder of our expansion is the same as in the Cramer result and therefore are optimal. Our result implies a moderate deviation principle for martingales. (c) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

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