Open Access
2015 Exponential inequalities for martingales with applications
Xiequan Fan, Ion Grama, Quansheng Liu
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Electron. J. Probab. 20: 1-22 (2015). DOI: 10.1214/EJP.v20-3496


The paper is devoted to establishing some general exponential inequalities for supermartingales. The inequalities improve or generalize many exponential inequalities of Bennett, Freedman, de la Peña, Pinelis and van de Geer. Moreover, our concentration inequalities also improve some known inequalities for sums of independent random variables. Applications associated with linear regressions, autoregressive processes and branching processes are also provided.


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Xiequan Fan. Ion Grama. Quansheng Liu. "Exponential inequalities for martingales with applications." Electron. J. Probab. 20 1 - 22, 2015.


Accepted: 4 January 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1320.60058
MathSciNet: MR3311214
Digital Object Identifier: 10.1214/EJP.v20-3496

Primary: 60E15
Secondary: 60G42

Keywords: autoregressive processes , Bernstein's inequality , changes of probability measure , De la Pena's inequality , Exponential inequality , Freedman's inequality , linear regressions , Martingales , Pinelis' inequality

Vol.20 • 2015
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