Short Communications

Limit Theorems for Functionals of Sample Functions of a Stationary Gaussian Process

Yu. M. Ryzhov

Kiev

Abstract: Let $\xi(t)$, $t\in[0,T]$, be a stationary Gaussian process with zero mean. We investigate the conditions for the functionals
$$ S_n=\sum_{k=1}^nf_n\biggl(\xi\biggl(\frac knT\biggr)\biggr)\frac Tn $$
to converge to the additive functionals
$$ J=\int_0^Tg(\xi(t))\,dt. $$


Received: 23.11.1965

 English version: Theory of Probability and its Applications, 1967, 12:2, 320–323

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