Large deviation exponential inequalities for supermartingales
Résumé
Let $(Xi,Fi)_i> 1$ be a sequence of supermartingale differences and let S$k = \sum^k_i=1 Xi$. We give an exponential moment condition under which $P(max_{1\leq k \les n Sk \geq n) = O(exp{−C_1 n }), n \rightarrow \infty$, where $\alpha \in (0, 1)$ is given and $C_1 > 0$ is a constant. We also show that the power is optimal under the given moment condition.