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Teoriya Veroyatnostei i ee Primeneniya, 1969, Volume 14, Issue 2, Pages 236–249
(Mi tvp1167)
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This article is cited in 3 scientific papers (total 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
Citation:
Yu. M. Ryzhov, “limit distributions of some Junctionals of a stationary Gaussian process”, Teor. Veroyatnost. i Primenen., 14:2 (1969), 236–249; Theory Probab. Appl., 14:2 (1969), 229–243
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https://www.mathnet.ru/eng/tvp1167 https://www.mathnet.ru/eng/tvp/v14/i2/p236
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Abstract page: | 136 | Full-text PDF : | 60 |
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