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August, 1983 Sharp Bounds on the Absolute Moments of a Sum of Two I.I.D. Random Variables
David C. Cox, J. H. B. Kemperman
Ann. Probab. 11(3): 765-771 (August, 1983). DOI: 10.1214/aop/1176993521


We determine the exact optimal bounds $A_p$ and $B_p$ such that $A_p\lbrack E|X|^p + E|Y|^p\rbrack \leq E|X + Y|^p \leq B_p\lbrack E|X|^p + E|Y|^p\rbrack,$ $(p \geq 1)$, whenever $X, Y$ are i.i.d. random variables with mean zero. We give examples of random variables attaining equality or nearly so. Exactly the same bounds $A_p$ and $B_p$ are obtained in the more general case where it is only assumed that $E(X \mid Y) = E(Y \mid X) = 0$.


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David C. Cox. J. H. B. Kemperman. "Sharp Bounds on the Absolute Moments of a Sum of Two I.I.D. Random Variables." Ann. Probab. 11 (3) 765 - 771, August, 1983.


Published: August, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0524.60019
MathSciNet: MR704563
Digital Object Identifier: 10.1214/aop/1176993521

Primary: 60E15
Secondary: 60G42 , 60G50

Keywords: Martingales , Sharp bounds on moments , sum of two i.i.d. random variables

Rights: Copyright © 1983 Institute of Mathematical Statistics


Vol.11 • No. 3 • August, 1983
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