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 Pe?a, 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.
展开▼
机译:本文致力于为超级市场建立一些一般的指数不等式。不等式改善或推广了Bennett,Freedman,de Peaa,Pinelis和van de Geer的许多指数不等式。此外,我们的集中不等式还改善了一些独立随机变量之和的已知不等式。还提供了与线性回归,自回归过程和分支过程相关的应用程序。
展开▼