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April, 1980 Monotonicity of an Integral of M. Klass
James Reeds
Ann. Probab. 8(2): 368-371 (April, 1980). DOI: 10.1214/aop/1176994783

Abstract

For each value of $\beta, 0 < \beta < 2$, the integral $$\int^\infty_{-\infty} \{1 - \exp(-x^{-2}\sin^2tx)\}|t|^{-1-\beta}dt$$ decreases monotonically as a function of $x, x > 0$. This result is useful in approximating the absolute $\beta$th moment of the sum of zero mean i.i.d. random variables.

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James Reeds. "Monotonicity of an Integral of M. Klass." Ann. Probab. 8 (2) 368 - 371, April, 1980. https://doi.org/10.1214/aop/1176994783

Information

Published: April, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0428.60059
MathSciNet: MR566600
Digital Object Identifier: 10.1214/aop/1176994783

Subjects:
Primary: 60G50
Secondary: 26A48, 44A10

Rights: Copyright © 1980 Institute of Mathematical Statistics

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Vol.8 • No. 2 • April, 1980
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