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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1967, Volume 12, Issue 3, Pages 433–443 (Mi tvp726)

On the Gaussian homogeneous fields with given conditional distributions

Yu. A. Rozanov

Moscow

Abstract: Let $\eta(t)$, $t\in E$, and $\zeta(t)\in E$, be two independent Gaussian fields in $r$-dimensional cancellated space $E$ and suppose that $\eta(t)$, $t\in E$, is a homogeneous field. Consider $\xi(t)=\eta(t)+\zeta(t)$, $t\in E$. Let $T\subset E$ be an arbitrary finite set and $\mathfrak B_T$ be the $\sigma$-algebra, generated by all random variables $\xi(t)$, $t\notin T$. The main question considered in this paper concerns the conditions for $\zeta(t)$, $t\in E$ , to be the field of conditional expectations of $\xi(t)$, $t\in E$, relative to $\mathfrak B=\bigcap\limits_T\mathfrak B_T$. Theorem 1, 2 solves the problem in the case when $\xi(t)$, $t\in E$, is a homogeneous field and theorem 4 when $\xi(t)$, $t\in E$, is a markovian field.

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English version:
Theory of Probability and its Applications, 1967, 12:3, 381–391

Bibliographic databases:

Citation: Yu. A. Rozanov, “On the Gaussian homogeneous fields with given conditional distributions”, Teor. Veroyatnost. i Primenen., 12:3 (1967), 433–443; Theory Probab. Appl., 12:3 (1967), 381–391

Citation in format AMSBIB
\Bibitem{Roz67} \by Yu.~A.~Rozanov \paper On the Gaussian homogeneous fields with given conditional distributions \jour Teor. Veroyatnost. i Primenen. \yr 1967 \vol 12 \issue 3 \pages 433--443 \mathnet{http://mi.mathnet.ru/tvp726} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=221582} \zmath{https://zbmath.org/?q=an:0212.20101} \transl \jour Theory Probab. Appl. \yr 1967 \vol 12 \issue 3 \pages 381--391 \crossref{https://doi.org/10.1137/1112050} 

• http://mi.mathnet.ru/eng/tvp726
• http://mi.mathnet.ru/eng/tvp/v12/i3/p433

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Yu. A. Rozanov, “On the theory of homogeneous random fields”, Math. USSR-Sb., 32:1 (1977), 1–18
2. “Absolute continuity between a Gibbs measure and its translate”, Theory Probab. Appl., 49:4 (2005), 713–724
3. Nowak E., Thilly E., “A local invariance principle for Gibbsian fields”, Statistics & Probability Letters, 76:18 (2006), 1975–1982