## Electronic Journal of Probability

### Exponential inequalities for martingales with applications

#### Abstract

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

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

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

https://projecteuclid.org/euclid.ejp/1465067107

Digital Object Identifier
doi:10.1214/EJP.v20-3496

Mathematical Reviews number (MathSciNet)
MR3311214

Zentralblatt MATH identifier
1320.60058

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

Rights

#### Citation

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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