Article PDF
References
Breiman, L.: Probability. Reading, Mass.: Addison-Wesley 1968
Chung, K.L.: The general theory of Markov processes according to Doeblin. Z. Wahrscheinlich-keitstheorie verw. Gebiete 2, 230–254 (1964)
Doeblin, W.: Sur les propriétés asymptotiques de mouvement régis par certains types de chaines simples. Bull. Math. Soc. Sci. Math. R.S. Roumanie 39, 1, 57–115; 2, 3–61 (1937)
Doeblin, W.: éléments d'une théorie générale des chaines simples constantes de Markoff. Ann. Sci. école Norm. Sup. (3) 57, No. 2, 61–111 (1940)
Doob, J.L.: Asymptotic properties of Markoff transition probabilities. Trans. Amer. Math. Soc. 63, 393–421 (1948)
Doob, J.L.: Stochastic processes. New York: Wiley and Sons 1953
Foguel, S.R.: The ergodic theorem for Markov processes. Israel J. Math. 4, 11–22 (1966)
Foguel, S.R.: The ergodic theory of Markov processes. New York: van Nostrand 1969
Harris, T. E.: The existence of stationary measures for certain Markov Processes. Proc. 3rd Berkeley Sympos. Math. Statist. Probab., II, 113–124 (1956)
Horowitz, S.: Some limit theorems for Markov processes. Israel J. Math. 6, 107–118 (1968)
Jacobs, K.: Zur Theorie der Markoffschen Prozesse. Math. Ann. 133, 375–399 (1957)
Jacobs, K.: Neuere Methoden und Ergebnisse der Ergodentheorie. Berlin-Göttingen-Heidelberg: Springer-Verlag 1960
Jain, N., Jamison, B.: Contributions to Doeblin's theory of Markov processes. Z. Wahrscheinlich-keitstheorie verw. Gebiete 8, 19–40 (1967)
Jamison, B., Orey, S.: Markov chains recurrent in the sense of Harris. Z. Wahrscheinlichkeits-theorie verw. Gebiete 8, 41–48 (1967)
Meyer, P.A.: Probability and Potentials. Waltham, Mass.: Blaisdell 1966
Neveu, J.: Bases mathématiques du calcul des probabilités. Paris: Masson 1964
Orey, S.: Recurrent Markov chains. Pacific J. Math. 9, 805–827 (1959)
Ornstein, D., Sucheston, L.: An operator theorem on L 1 convergence to zero with applications to Markov kernels. Ann. Math. Statist. 41, 1631–1639 (1970)
Yosida, K., Kakutani, S.: Operator-theoretical treatment of Markoff's process and mean ergodic theorem. Ann. Math. 42, 188–228 (1941)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Papangelou, F. A martingale approach to the convergence of the iterates of a transition function. Z. Wahrscheinlichkeitstheorie verw Gebiete 37, 211–226 (1977). https://doi.org/10.1007/BF00537489
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00537489