Geodesic
The invariance principle for stationary random fields satisfying the strong mixing condition
Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 2, pp. 358-364

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Let $\xi(u)$, $u\in R^q$, be a stationary random field satisfying the strong mixing condition, $V$ be an open set in $R^q$ with finite Lebesgue's measure $\mu(V)$, $$ T(V)=\int_V\xi(u)\,du, $$ The sufficient condition for the weak convergence of $$ \zeta_r(t)=(r^q\mu(V))^{-1/2}T(rt^{1/q}V),\qquad t\in[0,1], $$ to some Gaussian process $w_V(t)$ are obtained. 
@article{TVP_1982_27_2_a18,
     author = {V. V. Gorode{\cyrs}kiǐ},
     title = {The invariance principle for stationary random fields satisfying the strong mixing condition},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {358--364},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1982_27_2_a18/}
}
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V. V. Gorodeсkiǐ. The invariance principle for stationary random fields satisfying the strong mixing condition. Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 2, pp. 358-364. http://geodesic.mathdoc.fr/item/TVP_1982_27_2_a18/