This article is cited in 3 papers

Short Communications

The invariance principle for stationary random fields satisfying the strong mixing condition

V. V. Gorodeсkiĭ

Leningrad

Abstract: 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.

Received: 02.03.1979

 English version: Theory of Probability and its Applications, 1983, 27:2, 380–385

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