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Article Dans Une Revue Electronic Communications in Probability Année : 2012

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.
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Dates et versions

hal-00904496 , version 1 (14-11-2013)

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  • HAL Id : hal-00904496 , version 1

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Xiequan Fan, Ion Grama, Quansheng Liu. Large deviation exponential inequalities for supermartingales. Electronic Communications in Probability, 2012, 17 (59), pp.1-8. ⟨hal-00904496⟩
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