An Information-Theoretic Derivation of Certain Limit Relations for a Stationary Markov Chain

Previous article Next article An Information-Theoretic Derivation of Certain Limit Relations for a Stationary Markov ChainS. KullbackS. Kullbackhttps://doi.org/10.1137/0304035PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Kai Lai Chung, Markov chains with stationary transition probabilities, Die Grundlehren der mathematischen Wissenschaften, Bd. 104, Springer-Verlag, Berlin, 1960x+278 MR0116388 0092.34304 CrossrefGoogle Scholar[2] William Feller, An introduction to probability theory and its applications. Vol. I, John Wiley and Sons, Inc., New York, 1957xv+461, 2nd ed. MR0088081 0077.12201 Google Scholar[3] M. Fréchet, Recherches théoriques modernes sur le calcul des probabilités, Méthode des fonctions arbitraires. Théorie des événements en chaine dans le cas d'un nombre fini d'états possibles, Vol. II, Gauthier-Villars, Paris, 1938 0018.41301 Google Scholar[4] J. Hannan, I. Olkin, Consistency of maximum likelihood estimation of discrete distributions.Contributions to probability and statistics, Stanford Univ. Press, Stanford, Calif., 1960, 249–257 MR0120706 0173.46503 Google Scholar[5] David G. Kendall, Information theory and the limit-theorem for Markov chains and processes with a countable infinity of states, Ann. Inst. Statist. Math., 15 (1963), 137–143 MR0171317 0126.35901 CrossrefISIGoogle Scholar[6] Solomon Kullback, Information theory and statistics, John Wiley and Sons, Inc., New York, 1959xvii+395 MR0103557 0088.10406 Google Scholar[7] A. Rényi, On a measure of entropy and information, Proceedings of Fourth Berke-ley Symposium on Mathematical Statistics and Probability, Vol. 1, University of California Press, Berkeley, 1961, 547–561 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails An Extension of an Information-Theoretic Derivation of Certain Limit Relations for a Markov ChainS. Kullback18 July 2006 | SIAM Journal on Control, Vol. 5, No. 1AbstractPDF (147 KB) Volume 4, Issue 3| 1966SIAM Journal on Control History Submitted:08 December 1965Published online:18 July 2006 InformationCopyright © 1966 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0304035Article page range:pp. 454-459ISSN (print):0036-1402Publisher:Society for Industrial and Applied Mathematics