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arXiv · 1210.2198

Cramér large deviation expansions for martingales under Bernstein's condition

Xiequan Fan·Ion Grama·Quansheng Liu
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Abstract

By using the conjugate distribution technique of Cramér, we obtain some expansions of large deviation probabilities for martingales with differences satisfying the conditional Bernstein's condition. The expansions are of the same order as in the classical Cramér's large deviation result and are therefore optimal.

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Xiequan Fan, Ion Grama, Quansheng Liu. 2014-09-14. Cramér large deviation expansions for martingales under Bernstein's condition. https://doi.org/10.1016/j.spa.2013.06.010

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