| Abstract: |
| Let $(X _i,\mathcal{F}_i)_{i\geq1}$ be a sequence of martingale differences. Set $S_n=\sum_{i=1}^n X_i $ and $[ S]_n=\sum_{i=1}^n X_i^2.$ We prove a Cramer type moderate deviation expansion for $\mathbf{P}(S_n/\sqrt{[ S]_n} \geq x)$ as $n\to+\infty.$ Our results partly extend the earlier work of Jing, Shao and Wang (2003, Ann. Probab.) for independent random variables. |
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