This article is cited in 3 papers

limit distributions of some Junctionals of a stationary Gaussian process

Yu. M. Ryzhov

Kiev

Abstract: In this paper the limit distribution for sums
$$ S_n=\sum_{k=1}^nf_{nk}(\xi_k^{(n)}) $$
is considered, where $f_{nk}(x)$ are measurable functions,
$$ \xi_k^{(n)}=\xi\biggl(\frac knT\biggr)-\xi\biggl(\frac{k-1}nT\biggr),\quad k=1,2,\dots,n, $$
and $\xi(t)$, $t\in[0,T]$ is a stationary real-valued Gaussian process. Conditions are obtained under which the distributions of $S_k$ converge to a Gaussian and degenerate law.

Received: 26.10.1967

 English version: Theory of Probability and its Applications, 1969, 14:2, 229–243

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