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Large deviation exponential inequalities for supermartingales


 
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1. Title Title of document Large deviation exponential inequalities for supermartingales
 
2. Creator Author's name, affiliation, country Xiequan Fan; Université de Bretagne-Sud; France
 
2. Creator Author's name, affiliation, country Ion Grama; Université de Bretagne-Sud; France
 
2. Creator Author's name, affiliation, country Quansheng Liu; Université de Bretagne-Sud; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Large deviation; martingales; exponential inequality; Bernstein type inequality
 
3. Subject Subject classification 60F10; 60G42; 60E15
 
4. Description 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 $\alpha \in (0, 1)$ is given and $C_{1}>0$ is a constant. We also show that the power $\alpha$ is optimal under the given moment condition.
 
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7. Date (YYYY-MM-DD) 2012-12-12
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/2318
 
10. Identifier Digital Object Identifier 10.1214/ECP.v17-2318
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 17
 
12. Language English=en en
 
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