Article PDF
Avoid common mistakes on your manuscript.
References
Abrahamse, A.F.: The tail σ-field of a Markov chain. Ann. Math. Statist. 40, 127–136 (1969)
Athreya, K.B., Ney, P.E.: Branching Processes. New York: Springer 1972
Blackwell, D.: On transient Markov processes with a countable number of states and stationary transition probabilities. Ann. Math. Statist. 26, 654–658 (1955)
Breiman, L.: On transient Markov chains with application to the uniqueness problem for Markov processes. Ann. Math. Statist. 28, 499–503 (1957)
Chung, K.L.: Markov chains with stationary transition probabilities. 2nd Edition. New York: Springer 1967
Cohn, H.: On the tail events of a Markov chain. Z. Wahrscheinlichkeitstheorie verw. Gebiete 29, 65–72 (1974)
Cohn, H.: On the tail σ-field of the countable Markov chains. Rev. Roumaine Math. Pures Appl. 4, 850–858 (1976)
Cohn, H.: On the norming constants occurring in convergent Markov chains. Bull. Austral. Math. Soc. 17, 193–205 (1977)
Derriennic, Y.: Lois “zero ou deux” pour les processus de Markov. Applications aux marches aléatoires. Ann. Inst. H. Poincaré. Section B. XII, 2, 111–129 (1976)
Doob, J.L.: A Markov chain theorem. Probability and Statistics. (H. Cramér memorial volume) ed. U. Grenander, 50–57. Stockholm and New York: Almqvist and Wiksel, 1959
Dubuc, S.: Etats accessibles dans un processus de Galton-Watson. Canad. Math. Bull. 17, 111–113 (1974)
Griffeath, D.: Partial coupling and loss of memory for Markov chains. Ann. Probability 4, 850–858 (1976)
Küchler, U.: Über die σ-Algebra der asymptotischen Ereignisse bei diskreten Geburts- und Todesprozessen. Math. Nachr. 65, 321–329 (1975)
Loève, M.: Probability Theory. Third Edition. Princeton: Van Nostrand, 1963
Ornstein, D. and Sucheston, L.: An operator theorem on L 1 convergence to zero with applications to Markov kernels. Ann. Math. Statist. 41, 1631–1639 (1970)
Padmanabhan, A.R.: Convergence in probability and allied results. Math. Jap. 15, 111–117 (1970)
Schuh, H.-J., Barbour, A.: On the asymptotic behaviour of the branching processes with infinite mean. Advances Appl. Probability 9, 681–723 (1977)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cohn, H. On the invariant events of a markov chain. Z. Wahrscheinlichkeitstheorie verw Gebiete 48, 81–96 (1979). https://doi.org/10.1007/BF00534884
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00534884