In statistics of stochastic processes and random fields, a moment function or a cumulant of an estimate of either the correlation function or the spectral function can often contain an integral involving a cyclic product of kernels. We define and study this class of integrals and prove a Young-Hölder inequality. This inequality further enables us to study asymptotics of the above mentioned integrals in the situation where the kernels depend on a parameter. An application to the problem of estimation of the response function in a Volterra system is given.
@article{urn:eudml:doc:40366,
title = {A note on the application of integrals involving cyclic products of kernels.},
journal = {Q\"uestii\'o},
volume = {26},
year = {2002},
pages = {3-14},
zbl = {1040.62076},
mrnumber = {MR1924680},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40366}
}
Buldygin, Valery V.; Utzet, Frederic; Zaiats, Vladimir. A note on the application of integrals involving cyclic products of kernels.. Qüestiió, Tome 26 (2002) pp. 3-14. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40366/