Exponential inequalities for martingales with applications

Xiequan Fan; Ion Grama; Quansheng Liu

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arXiv · 1311.6273

Exponential inequalities for martingales with applications

Xiequan Fan·Ion Grama·Quansheng Liu

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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 provided. In particular, an interesting application of {de la Peña's} inequality to self-normalized deviations is also provided.

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Xiequan Fan, Ion Grama, Quansheng Liu. 2015-01-21. Exponential inequalities for martingales with applications. https://arxiv.org/abs/1311.6273

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