Prescribing a System of Random Variables by Conditional Distributions

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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 SectionsAbout[1] V. V. Sazonov, On perfect measures, Izv. Akad. Nauk SSSR Ser. Mat., 26 (1962), 391–414, (In Russian.) MR0181729 Google Scholar[2] 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 Scholar[3] 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 Scholar[4] 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 Scholar[5] Yu. A. Rozanov, On Gaussian fields with given conditional distributions, Theory Prob. Applications, 12 (1967), 381–391 10.1137/1112050 0212.20101 LinkGoogle Scholar[6] R. L. Dobrušin, Gibbsian random fields for lattice systems with pairwise interactions, Funkcional. Anal. i Priložen., 2 (1968), 31–43, (In Russian.) MR0250630 Google Scholar[7] 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 Scholar[8] R. L. Dobrušin, Gibbsian random fields. General case, Funkcional. Anal. i Priložen, 3 (1969), 27–35, (In Russian.) MR0239794 Google Scholar[9] 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 Scholar[10] 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 Scholar[11] M. G. Shnirman, On the problem of ergodicity for a Markov chain, “Problemy Kibernetiki”, 20 (1968), 115–122, (In Russian.) Google Scholar[12] 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 Scholar[13] 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 Scholar[14] A. L. Toom, A certain family of homogeneous nets of formal neurons, Dokl. Akad. Nauk SSSR, 183 (1968), 49–52, (In Russian.) MR0238614 Google Scholar[15] 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 Scholar[16] Yu. V. Prokhorov, Convergence of random processes and limit theorems in probability theory, Theory Prob. Applications, 1 (1956), 157–214 10.1137/1101016 LinkGoogle Scholar[17] 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 Scholar[18] I. A. Ibragimov and , Yu. V. Linnik, Independent and Stationary-Connected Variables, Izd-vo “Nauka”, Moscow, 1965, (In Russian.) Google Scholar[19] 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 Scholar[20] 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 Scholar[21] L. A. Ibragimov and , Yu. A. Rozanov, Gaussian Random Processes, Izd-vo “Nauka”, Moscow, 1970, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesC