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Teoriya Veroyatnostei i ee Primeneniya, 1967, Volume 12, Issue 2, Pages 370–372
(Mi tvp715)
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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
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
Linking options:
https://www.mathnet.ru/eng/tvp715 https://www.mathnet.ru/eng/tvp/v12/i2/p370
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Statistics & downloads: |
Abstract page: | 127 | Full-text PDF : | 63 |
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