Estimates of the Moments of Sums of Independent Random Variables

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1985 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:Theory of Probability & Its Applications, volume 29, pages 574-577 (issn: 0040-585X, eissn: 1095-7219,

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Authors: Pinelis, I. F.; Utev, S. A.;

doi: 10.1137/1129075

Estimates of the Moments of Sums of Independent Random Variables

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Abstract

Let \(X_ i\), \(i\geq 1\), be independent random variables with zero mean, \(S_ n=X_ 1+...+X_ n\), \(A_{t,n}=E(| X_ 1|^ t+...+| X_ n|^ t)\), \(B_ n=A^{1/2}_{2,n}\). An exact (but complicated) upper bound for \(E| S_ n|^ t\) is given in terms of \(A_{t,n}\) and \(B_ n\). The optimality of other earlier proved (and more simple) upper bounds for \(E| S_ n|^ t\) is investigated.

Keywords

Sums of independent random variables; random walks, Inequalities; stochastic orderings

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