A method of approximating expectations of functions of sums of independent random variables
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Publication:1153607
DOI10.1214/AOP/1176994415zbMath0463.60023OpenAlexW2084569901MaRDI QIDQ1153607
Publication date: 1981
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1214/aop/1176994415
Inequalities; stochastic orderings (60E15) Sums of independent random variables; random walks (60G50)
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A symmetrization-desymmetrization procedure for uniformly good approximation of expectations involving arbitrary sums of generalized \(U\)-statistics. ⋮ Decoupling and domination inequalities with application to Wald's identity for martingales ⋮ An improvement of Hoffmann-Jørgensen's inequality. ⋮ \(\Phi\)-moment inequalities for independent and freely independent random variables ⋮ A denormalized \(U\)-statistic which cannot be decoupled from some associated stopping times ⋮ Order of magnitude bounds for expectations of \(\Delta_2\)-functions of nonnegative random bilinear forms and generalized \(U\)-statistics ⋮ Moments of randomly stopped \(U\)-statistics ⋮ Maximal inequalities for additive processes ⋮ Uniformly accurate quantile bounds for sums of arbitrary independent random variables ⋮ The price of independence in a model with unknown dependence ⋮ Wald’s equation and asymptotic bias of randomly stopped 𝑈-statistics ⋮ Uniform bounds on the relative error in the approximation of upper quantiles for sums of arbitrary independent random variables
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