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Journal Articles Electronic Journal of Probability Year : 2015

Exponential inequalities for martingales with applications

Abstract

The paper is devoted to establishing some general exponential inequalities for super-martingales. 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 provided. In particular, an interesting application of de la Peña's inequality to self-normalized deviations is also provided.
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Dates and versions

hal-01108032 , version 1 (22-01-2015)

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Cite

Xiequan Fan, Ion Grama, Quansheng Liu. Exponential inequalities for martingales with applications. Electronic Journal of Probability, 2015, 20, pp.1 - 22. ⟨10.1214/EJP.v20-3496⟩. ⟨hal-01108032⟩
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