Some Classes of Homogeneous Denumerable Markov Processes

Abstract

Previous article Next article Some Classes of Homogeneous Denumerable Markov ProcessesR. L. DobrushinR. L. Dobrushinhttps://doi.org/10.1137/1102026PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThis paper contains a description of all denumerable homogeneous Markov processes with a fixed matrix of densities transition from a certain class of these matrices.[1] J. Doob, Stochastic Processes, Moscow-Leningrad, 1956, (Translated to Russian.) Google Scholar[2] Willy Feller, On the integro-differential equations of purely discontinuous Markoff processes, Trans. Amer. Math. Soc., 48 (1940), 488–515, Errata, 58 (1945), p. 474 MR0002697 0025.34704 CrossrefGoogle Scholar[3] R. L. Dobrushin, On conditions of regularity of stationary Markov processes with a denumerable number of possible states, Uspehi Matem. Nauk (N.S.), 7 (1952), 185–191, (In Russian.) MR0052056 Google Scholar[4] J. L. Doob, Markoff chains—denumerable case, Trans. Amer. Math. Soc., 58 (1945), 455–473 MR0013857 0063.01146 Google Scholar[5] Paul Lévy, Systèmes markoviens et stationnaires. Cas dénombrable, Ann. Sci. École Norm. Sup. (3), 68 (1951), 327–381 MR0047961 0044.33803 Google Scholar[6] David G. Kendall, Some further pathological examples in the theory of denumerable Markov processes, Quart. J. Math. Oxford Ser. (2), 7 (1956), 39–56 MR0088832 0075.14101 CrossrefGoogle Scholar[7] David Blackwell, On transient Markov processes with a countable number of states and stationary transition probabilities, Ann. Math. Statist., 26 (1955), 654–658 MR0075479 0066.11303 CrossrefGoogle Scholar[8] A. D. Venttsel', Semigroups of operators corresponding to generalizations of differential operators of the second order, Dokl. Akad. Nauk SSSR, III (1956), 269–273, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Discontinuous Markov ProcessesE. B. Dynkin17 July 2006 | Theory of Probability & Its Applications, Vol. 3, No. 1AbstractPDF (1726 KB) Volume 2, Issue 3| 1957Theory of Probability & Its Applications History Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1102026Article page range:pp. 366-369ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics