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JOURNALS // Teoriya Veroyatnostei i ee Primeneniya // Archive

Teor. Veroyatnost. i Primenen., 1970 Volume 15, Issue 2, Pages 304–309 (Mi tvp1813)

This article is cited in 3 papers

Short Communications

On connection between two characteristics of dependence of Gaussian random vectors

I. A. Ibragimova, Yu. A. Rozanovb

a Leningrad
b Moscow

Abstract: Let $\xi$ and $\eta$ be Gaussian random vectors with distributions $\mathscr P_1(dx)$ and $\mathscr P_2(dy)$ respectvely, and with joint distribution $\mathscr P_{12}(dxdy)$. Let $I$ be the information about $\eta$, containing in $\xi$. Set
$$ V=\operatorname{Var}(\mathscr P_{12}-\mathscr P_1\times\mathscr P_2). $$
In the paper connection between $I$ and $V$ is under investigation.

Received: 05.06.1969


 English version:
Theory of Probability and its Applications, 1970, 15:2, 295–299

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