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Teoriya Veroyatnostei i ee Primeneniya, 1967, Volume 12, Issue 2, Pages 370–372 (Mi tvp715)  
Short Communications

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

Yu. M. Ryzhov

Kiev
Full-text PDF (173 kB)
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, Volume 12, Issue 2, Pages 320–323
DOI: https://doi.org/10.1137/1112038
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Yu. M. Ryzhov, “Limit Theorems for Functionals of Sample Functions of a Stationary Gaussian Process”, Teor. Veroyatnost. i Primenen., 12:2 (1967), 370–372; Theory Probab. Appl., 12:2 (1967), 320–323
Citation in format AMSBIB
\Bibitem{Ryz67}
\by Yu.~M.~Ryzhov
\paper Limit Theorems for Functionals of Sample Functions of a~Stationary Gaussian Process
\jour Teor. Veroyatnost. i Primenen.
\yr 1967
\vol 12
\issue 2
\pages 370--372
\mathnet{http://mi.mathnet.ru/tvp715}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=217867}
\zmath{https://zbmath.org/?q=an:0174.50001}
\transl
\jour Theory Probab. Appl.
\yr 1967
\vol 12
\issue 2
\pages 320--323
\crossref{https://doi.org/10.1137/1112038}
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