The Local Limit Theorem for Markov Chains and Regularity Conditions

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Previous article Next article The Local Limit Theorem for Markov Chains and Regularity ConditionsB. M. GurevichB. M. Gurevichhttps://doi.org/10.1137/1113019PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. N. Kolmogorov, A new metric invariant of transient dynamical systems and automorphisms in Lebesgue spaces, Dokl. Akad. Nauk SSSR (N.S.), 119 (1958), 861–864, (In Russian.) MR0103254 0083.10602 Google Scholar[2] I. A. Ibragimov and , Yu. V. Linnik, Independent and Stationarily Dependent Variables, “Nauka”, Moscow, 1965, 524–, (In Russian.) Google Scholar[3] B. M. Gurevich, On one class of special automorphisms and special flows, Dokl. Akad. Nauk SSSR, 153 (1963), 754–757, (In Russian.) Google Scholar[4] A. N. Kolmogorov, A local limit theorem for classical Markov chains, Izvestiya Akad. Nauk SSSR. Ser. Mat., 13 (1949), 281–300, (In Russian.) MR0031216 Google Scholar[5] I. Z. Rozenknop, On some properties of collections of closed paths in a system with n states and given connections among them, Izvestiya Akad. Nauk SSSR. Ser. Mat., 14 (1950), 95–100, (In Russian.) MR0033468 Google Scholar[6] I. V. Čulanovskii˘, On cycles in Markov chains, Doklady Akad. Nauk SSSR (N.S.), 69 (1949), 301–304, (In Russian.) MR0032120 Google Scholar[7] J. L. Doob, Stochastic processes, John Wiley & Sons Inc., New York, 1953viii+654 MR0058896 0053.26802 Google Scholar[8] Ya. G. Sinai, Dynamic systems and stationary Markov processes, Theory Prob. Applications, 4 (1960), 305–308 10.1137/1105029 LinkGoogle Scholar[9] V. A. RoKhlin, New progress in the theory of transformations with invariant measure, Uspekhi Mat. Nauk, 15 (1960), 3–26, (In Russian.) Google Scholar[10] B. M. Gurevich, Some conditions for the existence of K-partitions for special flows, Trudy Mosk. Matem. Ob-va, 17 (1967), 90–117, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails On the $\sigma $-Algebra of Symmetric Events for a Countable Markov ChainL. A. Grigorenko17 July 2006 | Theory of Probability & Its Applications, Vol. 24, No. 1AbstractPDF (723 KB) Volume 13, Issue 1| 1968Theory of Probability & Its Applications History Submitted:08 October 1966Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1113019Article page range:pp. 182-188ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics