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.
Publié le : 1980-04-14
Classification:
Laplace transform,
total positivity,
variation diminishing,
60G50,
44A10,
26A48
@article{1176994783,
author = {Reeds, James},
title = {Monotonicity of an Integral of M. Klass},
journal = {Ann. Probab.},
volume = {8},
number = {6},
year = {1980},
pages = { 368-371},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994783}
}
Reeds, James. Monotonicity of an Integral of M. Klass. Ann. Probab., Tome 8 (1980) no. 6, pp. 368-371. http://gdmltest.u-ga.fr/item/1176994783/