Electronic Journal of Probability

Exponential inequalities for martingales with applications

Xiequan Fan, Ion Grama, and Quansheng Liu

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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.

Article information

Electron. J. Probab., Volume 20 (2015), paper no. 1, 22 pp.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60G42: Martingales with discrete parameter

exponential inequality martingales changes of probability measure Freedman's inequality De la Pena's inequality Pinelis' inequality Bernstein's inequality linear regressions autoregressive processes

This work is licensed under aCreative Commons Attribution 3.0 License.


Fan, Xiequan; Grama, Ion; Liu, Quansheng. Exponential inequalities for martingales with applications. Electron. J. Probab. 20 (2015), paper no. 1, 22 pp. doi:10.1214/EJP.v20-3496. https://projecteuclid.org/euclid.ejp/1465067107

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