Fan, Xiequan; Grama, Ion; Liu, Quansheng Exponential inequalities for martingales with applications. (English) Zbl 1320.60058 Electron. J. Probab. 20, Paper No. 1, 22 p. (2015). Summary: The paper is devoted to establishing some general exponential inequalities for supermartingales. The inequalities improve or generalize many exponential inequalities of G. Bennett [J. Am. Stat. Assoc. 57, No. 297, 33–45 (1962; Zbl 0104.11905)], D. A. Freedman [Ann. Probab. 3, 100–118 (1975; Zbl 0313.60037)], V. H. de la Peña [Ann. Probab. 27, No. 1, 537–564 (1999; Zbl 0942.60004)], I. Pinelis [Ann. Probab. 22, No. 4, 1679–1706 (1994; Zbl 0836.60015)] and S. van de Geer [Ann. Stat. 23, No. 5, 1779–1801 (1995; Zbl 0852.60019); in: Empirical process techniques for dependent data. Boston, MA: Birkhäuser. 161–169 (2002; Zbl 1027.60013)]. 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. Cited in 16 Documents MSC: 60E15 Inequalities; stochastic orderings 60G42 Martingales with discrete parameter Keywords:exponential inequality; martingales; changes of probability measure; Freedman’s inequality; de la Peña’s inequality; Pinelis’ inequality; Bernstein’s inequality; linear regressions; autoregressive processes Citations:Zbl 0104.11905; Zbl 0313.60037; Zbl 0942.60004; Zbl 0836.60015; Zbl 0852.60019; Zbl 1027.60013 PDFBibTeX XMLCite \textit{X. Fan} et al., Electron. J. Probab. 20, Paper No. 1, 22 p. (2015; Zbl 1320.60058) Full Text: DOI arXiv