English

Cram\'er large deviation expansions for martingales under Bernstein's condition

Probability 2014-09-16 v3

Abstract

By using the conjugate distribution technique of Cram\'er, 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 Cram\'er's large deviation result and are therefore optimal.

Keywords

Cite

@article{arxiv.1210.2198,
  title  = {Cram\'er large deviation expansions for martingales under Bernstein's condition},
  author = {Xiequan Fan and Ion Grama and Quansheng Liu},
  journal= {arXiv preprint arXiv:1210.2198},
  year   = {2014}
}

Comments

26 pages

R2 v1 2026-06-21T22:17:51.882Z