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This article is cited in 3 scientific papers (total in 3 papers)
A functional central limit theorem for integrals of stationary mixing random fields
J. Kampf, E. Spodarev Institute of Stochastics, Ulm University, Germany
Abstract:
We prove a functional central limit theorem for the integrals
$\int_W f(X(t))\, dt$, where $(X(t))_{t\in\mathbf{R}^d}$
is a stationary mixing random field and the stochastic process is indexed by the function $f$,
as the integration domain $W$ grows unboundedly in the Van Hove sense.
We also discuss properties of the covariance function of the limiting Gaussian process.
Keywords:
functional central limit theorem, $\mathrm{GB}$-set, Meixner system, mixing, random field.
Received: 17.03.2016 Revised: 17.05.2017 Accepted: 22.05.2017
Citation:
J. Kampf, E. Spodarev, “A functional central limit theorem for integrals of stationary mixing random fields”, Teor. Veroyatnost. i Primenen., 63:1 (2018), 167–185; Theory Probab. Appl., 63:1 (2018), 135–150
Linking options:
https://www.mathnet.ru/eng/tvp5161https://doi.org/10.4213/tvp5161 https://www.mathnet.ru/eng/tvp/v63/i1/p167
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