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2012 Large deviation exponential inequalities for supermartingales
Xiequan Fan, Ion Grama, Quansheng Liu
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Electron. Commun. Probab. 17: 1-8 (2012). DOI: 10.1214/ECP.v17-2318

Abstract

Let $(X_{i}, \mathcal{F}_{i})_{i\geq 1}$ be a sequence of supermartingale differences and let $S_k=\sum_{i=1}^k X_i$. We give an exponential moment condition under which $\mathbb{P}( \max_{1\leq k \leq n} S_k \geq n)=O(\exp\{-C_1 n^{\alpha}\}),$ $n\rightarrow \infty, $ where $\alpha \in $ is given and $C_{1}>0$ is a constant. We also show that the power $\alpha$ is optimal under the given moment condition.

Citation

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Xiequan Fan. Ion Grama. Quansheng Liu. "Large deviation exponential inequalities for supermartingales." Electron. Commun. Probab. 17 1 - 8, 2012. https://doi.org/10.1214/ECP.v17-2318

Information

Accepted: 12 December 2012; Published: 2012
First available in Project Euclid: 7 June 2016

zbMATH: 1312.60016
MathSciNet: MR3005732
Digital Object Identifier: 10.1214/ECP.v17-2318

Subjects:
Primary: 60F10
Secondary: 60E15, 60G42

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