The Annals of Probability

Monotonicity of an Integral of M. Klass

James Reeds

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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.

Article information

Source
Ann. Probab., Volume 8, Number 2 (1980), 368-371.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994783

Digital Object Identifier
doi:10.1214/aop/1176994783

Mathematical Reviews number (MathSciNet)
MR566600

Zentralblatt MATH identifier
0428.60059

JSTOR
links.jstor.org

Subjects
Primary: 60G50: Sums of independent random variables; random walks
Secondary: 44A10: Laplace transform 26A48: Monotonic functions, generalizations

Keywords
Laplace transform total positivity variation diminishing

Citation

Reeds, James. Monotonicity of an Integral of M. Klass. Ann. Probab. 8 (1980), no. 2, 368--371. doi:10.1214/aop/1176994783. https://projecteuclid.org/euclid.aop/1176994783


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