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Previous article Next article Prescribing a System of Random Variables by Conditional DistributionsR. L. DobrushinR. L. Dobrushinhttps: //doi. org/10. 1137/1115049PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 V. V. Sazonov, On perfect measures, Izv. Akad. Nauk SSSR Ser. Mat. , 26 (1962), 391–414, (In Russian. ) MR0181729 Google Scholar2 K. R. Parthasarathy, Probability measures on metric spaces, Probability and Mathematical Statistics, No. 3, Academic Press Inc. , New York, 1967xi+276 MR0226684 0153. 19101 CrossrefGoogle Scholar3 M. B. Averincev, A certain method of describing random fields with a discrete argument, Problemy Peredači Informacii, 6 (1970), 100–108, (In Russian. ) MR0329038 Google Scholar4 R. L. Dobrushin, The description of a random field by means of conditional probabilities and conditions of its regularity, Theory Prob. Applications, 13 (1968), 197–224 10. 1137/1113026 LinkGoogle Scholar5 Yu. A. Rozanov, On Gaussian fields with given conditional distributions, Theory Prob. Applications, 12 (1967), 381–391 10. 1137/1112050 0212. 20101 LinkGoogle Scholar6 R. L. Dobrušin, Gibbsian random fields for lattice systems with pairwise interactions, Funkcional. Anal. i Priložen. , 2 (1968), 31–43, (In Russian. ) MR0250630 Google Scholar7 R. L. Dobrushin, The problem of uniqueness for a Gibbsian random field and the problem of phase transitions, Funktsional'nyi Analiz i evo Primen, 2 (1968), 44–57, (In Russian. ) 0192. 61702 Google Scholar8 R. L. Dobrušin, Gibbsian random fields. General case, Funkcional. Anal. i Priložen, 3 (1969), 27–35, (In Russian. ) MR0239794 Google Scholar9 R. L. Dobrushin, Gibbsian random fields for particles without a solid core, Funktsional'nyi Analiz i evo Primen. , 4 (1970), 101–118, (In Russian. ) Google Scholar10 O. N. Stavskaja and, I. I. Pjateckii˘-Šapiro, Homogeneous networks of spontaneously active elements, Problemy Kibernet. No. , 20 (1968), 91–106 MR0286511 0191. 31102 Google Scholar11 M. G. Shnirman, On the problem of ergodicity for a Markov chain, “Problemy Kibernetiki”, 20 (1968), 115–122, (In Russian. ) Google Scholar12 L. N. Vasershtein, Markov processes over denumerable products of spaces describing large system of automata, Problemy Peredači Informacii, 5 (1969), 64–72, (In Russian. ) MR0314115 Google Scholar13 Ju. K. Beljaev, , Ju. I. Gromak and, V. A. Malyšev, Invariant random Boolean fields, Mat. Zametki, 6 (1969), 555–566, (In Russian. ) MR0258113 0201. 18605 Google Scholar14 A. L. Toom, A certain family of homogeneous nets of formal neurons, Dokl. Akad. Nauk SSSR, 183 (1968), 49–52, (In Russian. ) MR0238614 Google Scholar15 N. B. Vasil'ev, The limiting behavior of a certain random medium, Problemy Peredači Informacii, 5 (1969), 68–74, (In Russian. ) MR0309661 0284. 60097 Google Scholar16 Yu. V. Prokhorov, Convergence of random processes and limit theorems in probability theory, Theory Prob. Applications, 1 (1956), 157–214 10. 1137/1101016 LinkGoogle Scholar17 Nelson Dunford and, Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc. , New York, 1958xiv+858 MR0117523 0084. 10402 Google Scholar18 I. A. Ibragimov and, Yu. V. Linnik, Independent and Stationary-Connected Variables, Izd-vo “Nauka”, Moscow, 1965, (In Russian. ) Google Scholar19 R. L. Dobrushin, Central limit theorem for nonstationary Markov chains, I, II, Theory Prob. Applications, 1 (1956), , I, 1, pp. 65–80; II, 4, pp. 329–383 Google Scholar20 L. N. Vaserštei˘n and, A. M. Leontovič, Invariant measures of certain Markov operators that describe a homogeneous random medium, Problemy Peredači Informacii, 6 (1970), 71–80, (In Russian. ) MR0530400 Google Scholar21 L. A. Ibragimov and, Yu. A. Rozanov, Gaussian Random Processes, Izd-vo “Nauka”, Moscow, 1970, (In Russian. ) Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Multispectral and hyperspectral image fusion in remote sensing: A surveyInformation Fusion, Vol. 89 | 1 Jan 2023 Cross Ref Strict Kantorovich contractions for Markov chains and Euler schemes with general noiseStochastic Processes and their Applications, Vol. 151 | 1 Sep 2022 Cross Ref Quantum Concentration InequalitiesAnnales Henri Poincaré, Vol. 23, No. 9 | 21 April 2022 Cross Ref A Functional Central Limit Theorem for Polaron Path MeasuresCommunications on Pure and Applied Mathematics, Vol. 9 | 12 August 2022 Cross Ref A Wasserstein-based measure of conditional dependenceBehaviormetrika, Vol. 49, No. 2 | 25 June 2022 Cross Ref Identifying biases in the global placement of river gaugesNature Sustainability, Vol. 5, No. 7 | 25 April 2022 Cross Ref Assessing placement bias of the global river gauge networkNature Sustainability, Vol. 5, No. 7 | 25 April 2022 Cross Ref Implementation of the regularized Rudin-Osher-Fatemi denoising method in the coherent wave burst pipeline for gravitational-wave data analysisPhysical Review D, Vol. 106, No. 2 | 19 July 2022 Cross Ref Correlation decay for hard spheres via Markov chainsThe Annals of Applied Probability, Vol. 32, No. 3 | 1 Jun 2022 Cross Ref Memory drives the formation of animal home ranges: Evidence from a reintroductionEcology Letters, Vol. 25, No. 4 | 31 January 2022 Cross Ref Classical Particles in the Continuum Subjected to High Density Boundary ConditionsAnnales Henri Poincaré, Vol. 37 | 20 January 2022 Cross Ref OverlapNet: a siamese network for computing LiDAR scan similarity with applications to loop closing and localizationAutonomous Robots, Vol. 46, No. 1 | 5 August 2021 Cross Ref Model Compression Using Optimal Transport2022 IEEE/CVF Winter Conference on Applications of Computer Vision (WACV) | 1 Jan 2022 Cross Ref Ensemble Riemannian data assimilation: towards large-scale dynamical systemsNonlinear Processes in Geophysics, Vol. 29, No. 1 | 18 February 2022 Cross Ref Convergence of Spectral Triples on Fuzzy Tori to Spectral Triples on Quantum ToriCommunications in Mathematical Physics, Vol. 388, No. 2 | 20 August 2021 Cross Ref Optimal Representation of the Nuclear Ensemble: Application to Electronic SpectroscopyJournal of Chemical Theory and Computation, Vol. 17, No. 10 | 20 September 2021 Cross Ref Assessing data change in scientific datasetsConcurrency and Computation: Practice and Experience, Vol. 33, No. 16 | 2 March 2021 Cross Ref Spectral Independence in High-Dimensional Expanders and Applications to the Hardcore ModelNima Anari, Kuikui Liu, and Shayan Oveis GharanSIAM Journal on Computing, Vol. 0, No. 0 | 12 July 2021AbstractPDF (704 KB) Geometric models reveal behavioural and neural signatures of transforming experiences into memoriesNature Human Behaviour, Vol. 5, No. 7 | 11 February 2021 Cross Ref Phase transitions in random mixtures of elementary cellular automataPhysica A: Statistical Mechanics and its Applications, Vol. 573 | 1 Jul 2021 Cross Ref The measurement of relations on belief functions based on the Kantorovich problem and the Wasserstein metricInternational Journal of Approximate Reasoning, Vol. 131 | 1 Apr 2021 Cross Ref A generative adversarial network for travel times imputation using trajectory dataComputer-Aided Civil and Infrastructure Engineering, Vol. 36, No. 2 | 24 June 2020 Cross Ref Poisson approximation in terms of the Gini–Kantorovich distanceExtremes, Vol. 174 | 8 January 2021 Cross Ref Stability in Distribution of Path-Dependent Hybrid DiffusionDang H. 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