Geodesic
A functional central limit theorem for integrals of stationary mixing random fields
Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 1, pp. 167-185

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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. 
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     author = {J. Kampf and E. Spodarev},
     title = {A functional central limit theorem for integrals of stationary mixing random fields},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {167--185},
     publisher = {mathdoc},
     volume = {63},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2018_63_1_a7/}
}
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J. Kampf; E. Spodarev. A functional central limit theorem for integrals of stationary mixing random fields. Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 1, pp. 167-185. http://geodesic.mathdoc.fr/item/TVP_2018_63_1_a7/