On Gaussian Fields with Given Conditional Distributions

Previous article Next article On Gaussian Fields with Given Conditional DistributionsYu. A. RosanovYu. A. Rosanovhttps://doi.org/10.1137/1112050PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 Paul Lévy, Processus Stochastiques et Mouvement Brownien. Suivi d'une note de M. Loève, Gauthier-Villars, Paris, 1948, 365– MR0029120 0034.22603 Google Scholar2 A. M. Yaglom, Some classes of random fields in n-dimensional space related to stationary random processes, Theory Prob. Applications, 2 (1957), 273–320 10.1137/1102021 LinkGoogle Scholar3 Yu. A. Rozanov, On interpolation of stationary processes with discrete time, Dokl. Akad. Nauk SSSR, 130 (1960), 730–733, (In Russian.) Google Scholar4 Henry Helson and , David Lowdenslager, Prediction theory and Fourier series in several variables, Acta Math., 99 (1958), 165–202 MR0097688 0082.28201 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails BibliographySojourns and Extremes of Stochastic Processes | 31 October 2017 Cross Ref ReferencesStatistics for Spatial Data | 7 April 2015 Cross Ref Gaussian Process, Conditional and SimultaneousEncyclopedia of Environmetrics | 15 September 2006 Cross Ref Mathematical statistics and computer visionImage and Vision Computing, Vol. 30, No. 8 | 1 Aug 2012 Cross Ref Statistical Analysis of Spatio-Temporal Models and Their ApplicationsTime Series Analysis: Methods and Applications | 1 Jan 2012 Cross Ref A local invariance principle for Gibbsian fieldsStatistics & Probability Letters, Vol. 76, No. 18 | 1 Dec 2006 Cross Ref Adaptive Segmentation of Textured Images by Using the Coupled Markov Random Field ModelIEEE Transactions on Image Processing, Vol. 15, No. 11 | 1 Nov 2006 Cross Ref Modified Whittle estimation of multilateral models on a latticeJournal of Multivariate Analysis, Vol. 97, No. 5 | 1 May 2006 Cross Ref Absolute Continuity between a Gibbs Measure and Its TranslateTheory of Probability & Its Applications, Vol. 49, No. 4 | 25 July 2006AbstractPDF (185 KB)Ch. 13. 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Bayesian estimators based on Markov random fieldsIEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 17, No. 3 | 1 Mar 1995 Cross Ref Towards Perceptual Control of Markov Random Field TexturesPerceptual Issues in Visualization | 1 Jan 1995 Cross Ref Image Estimation Using 2D Noncausal Gauss-Markov Random Field ModelsDigital Image Restoration | 1 Jan 1991 Cross Ref Discrete-index Markov-type random processesProceedings of the IEEE, Vol. 77, No. 10 | 1 Oct 1989 Cross Ref Remarks on the non-compact spin systemsJournal of Physics A: Mathematical and General, Vol. 22, No. 11 | 1 January 1999 Cross Ref Two-Dimensional Discrete Gaussian Markov Random Field Models for Image ProcessingIETE Journal of Research, Vol. 35, No. 2 | 2 June 2015 Cross Ref Multi-dimensional multivariate Gaussian Markov random fields with application to image processingJournal of Multivariate Analysis, Vol. 24, No. 2 | 1 Feb 1988 Cross Ref Poisson and extreme value limit theorems for Markov random fieldsAdvances in Applied Probability, Vol. 19, No. 01 | 1 July 2016 Cross Ref Poisson and extreme value limit theorems for Markov random fieldsAdvances in Applied Probability, Vol. 19, No. 1 | 1 July 2016 Cross Ref Two-dimensional spectrum estimation using noncausal autoregressive modelsIEEE Transactions on Information Theory, Vol. 32, No. 2 | 1 Mar 1986 Cross Ref Classification of textures using Gaussian Markov random fieldsIEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 33, No. 4 | 1 Aug 1985 Cross Ref A model-based approach for estimation of two-dimensional maximum entropy power spectraIEEE Transactions on Information Theory, Vol. 31, No. 1 | 1 Jan 1985 Cross Ref Characterization and estimation of two-dimensional ARMA modelsIEEE Transactions on Information Theory, Vol. 30, No. 5 | 1 Sep 1984 Cross Ref BibliographyFoundations of the Probabilistic Mechanics of Discrete Media | 1 Jan 1984 Cross Ref Recursive contextual classification using a spatial stochastic modelPattern Recognition, Vol. 16, No. 1 | 1 Jan 1983 Cross Ref On the variance of the sample correlation between two independent lattice processesJournal of Applied Probability, Vol. 18, No. 04 | 14 July 2016 Cross Ref On the variance of the sample correlation between two independent lattice processesJournal of Applied Probability, Vol. 18, No. 4 | 14 July 2016 Cross Ref Journal of the Royal Statistical Society: Series B (Methodological), Vol. 43, No. 3 | 1981 Cross Ref Almost sure entropy and the variational principle for random fields with unbounded state spaceZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 58, No. 1 | 1 Jan 1981 Cross Ref Thermodynamics and statistical analysis of Gaussian random fieldsZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 58, No. 3 | 1 Jan 1981 Cross Ref On a Property of Homogeneous Gaussian L-FieldsTheory of Probability & Its Applications, Vol. 24, No. 3 | 17 July 2006AbstractPDF (395 KB)HYPOTHETICAL 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IEEE International Conference on Acoustics, Speech, and Signal Processing Cross Ref Simultaneous confidence bands for a class of 2-D spectral estimatesICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing Cross Ref ReferencesGibbs Measures and Phase Transitions Cross Ref Image identification and restoration using 2-d noncasual markovian random field modelsProceedings. ICCON IEEE International Conference on Control and Applications Cross Ref The Description of a Random Field by Means of Conditional Probabilities and Conditions of Its RegularityTheory of Probability & Its Applications, Vol. 13, No. 2 | 28 July 2006AbstractPDF (2822 KB) Volume 12, Issue 3| 1967Theory of Probability & Its Applications347-533 History Submitted:30 January 1967Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1112050Article page range:pp. 381-391ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics