# A note on the application of integrals involving cyclic products of kernels.

Valery V. Buldygin; Frederic Utzet; Vladimir Zaiats

Qüestiió (2002)

- Volume: 26, Issue: 1-2, page 3-14
- ISSN: 0210-8054

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topBuldygin, Valery V., Utzet, Frederic, and Zaiats, Vladimir. "A note on the application of integrals involving cyclic products of kernels.." Qüestiió 26.1-2 (2002): 3-14. <http://eudml.org/doc/40366>.

@article{Buldygin2002,

abstract = {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.},

author = {Buldygin, Valery V., Utzet, Frederic, Zaiats, Vladimir},

journal = {Qüestiió},

keywords = {Procesos estocásticos; Inferencia no paramétrica; Ecuaciones integrales estocásticas; Kernel; Convergencia asintótica; integral involving cyclic products of kernels; cumulants; Young-Hölder inequality; cross-correlogram; asymptotic normality},

language = {eng},

number = {1-2},

pages = {3-14},

title = {A note on the application of integrals involving cyclic products of kernels.},

url = {http://eudml.org/doc/40366},

volume = {26},

year = {2002},

}

TY - JOUR

AU - Buldygin, Valery V.

AU - Utzet, Frederic

AU - Zaiats, Vladimir

TI - A note on the application of integrals involving cyclic products of kernels.

JO - Qüestiió

PY - 2002

VL - 26

IS - 1-2

SP - 3

EP - 14

AB - 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.

LA - eng

KW - Procesos estocásticos; Inferencia no paramétrica; Ecuaciones integrales estocásticas; Kernel; Convergencia asintótica; integral involving cyclic products of kernels; cumulants; Young-Hölder inequality; cross-correlogram; asymptotic normality

UR - http://eudml.org/doc/40366

ER -