Electronic Journal of Probability

Exponential inequalities for martingales with applications

Xiequan Fan, Ion Grama, and Quansheng Liu

Full-text: Open access

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

Permanent link to this document
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

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

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

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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