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Mat. Sb. (N.S.), 1977, Volume 103(145), Number 4(8), Pages 590–613 (Mi msb2931)  

This article is cited in 6 scientific papers (total in 6 papers)

Markov random fields and stochastic partial differential equations

Yu. A. Rozanov


Abstract: In this paper we study some classes of Markov random fields. In particular, it is proved that the solution of a linear stochastic partial differential equation is a Markov field.
Bibliography: 7 titles.

Full text: PDF file (2165 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1977, 32:4, 515–534

Bibliographic databases:

UDC: 519.2
MSC: 60G20, 60J25, 60H15
Received: 13.04.1977

Citation: Yu. A. Rozanov, “Markov random fields and stochastic partial differential equations”, Mat. Sb. (N.S.), 103(145):4(8) (1977), 590–613; Math. USSR-Sb., 32:4 (1977), 515–534

Citation in format AMSBIB
\Bibitem{Roz77}
\by Yu.~A.~Rozanov
\paper Markov random fields and stochastic partial differential equations
\jour Mat. Sb. (N.S.)
\yr 1977
\vol 103(145)
\issue 4(8)
\pages 590--613
\mathnet{http://mi.mathnet.ru/msb2931}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=467916}
\zmath{https://zbmath.org/?q=an:0364.60100}
\transl
\jour Math. USSR-Sb.
\yr 1977
\vol 32
\issue 4
\pages 515--534
\crossref{https://doi.org/10.1070/SM1977v032n04ABEH002404}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1977GL81400008}


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  • http://mi.mathnet.ru/eng/msb/v145/i4/p590

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
    Cycle of papers

    This publication is cited in the following articles:
    1. Yu. A. Rozanov, “On the paper “Markov random fields and stochastic partial differential equations””, Math. USSR-Sb., 35:1 (1979), 157–164  mathnet  crossref  mathscinet  zmath  isi
    2. P. E. Dedik, M. A. Shubin, “Random pseudodifferential operators and the stabilization of solutions of parabolic equations with random coefficients”, Math. USSR-Sb., 41:1 (1982), 33–52  mathnet  crossref  mathscinet  zmath
    3. Michael Röckner, “Markov property of generalized fields and axiomatic potential theory”, Math Ann, 264:2 (1983), 153  crossref  mathscinet  zmath  isi
    4. Finn Lindgren, Håvard Rue, Johan Lindström, “An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach”, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 73:4 (2011), 423  crossref
    5. Daniel Simpson, Finn Lindgren, Håvard Rue, “Think continuous: Markovian Gaussian models in spatial statistics”, Spatial Statistics, 1 (2012), 16  crossref
    6. Assing S., Bichard J., “On the Spatial Dynamics of the Solution to the Stochastic Heat Equation”, Electron. J. Probab., 18 (2013), 70, 1–32  crossref  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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