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Contributions to the theory of Markov chains. II. (English) Zbl 0058.34602


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[1] Kai Lai Chung, Contributions to the theory of Markov chains, J. Research Nat. Bur. Standards 50 (1953), 203 – 208. · Zbl 0053.27201
[2] K. L. Chung and W. H. J. Fuchs, On the distribution of values of sums of random variables, Mem. Amer. Math. Soc. No. 6 (1951), 12. · Zbl 0042.37502
[3] Wolfgang Doeblin, Sur deux problèmes de M. Kolmogoroff concernant les chaînes dénombrables, Bull. Soc. Math. France 66 (1938), 210 – 220 (French). · Zbl 0020.14604
[4] -, Thèse, Paris (printed in Bucharest), 1938.
[5] J. L. Doob, The law of large numbers for continuous stochastic processes, Duke Math. J. 6 (1940), 290 – 306. · JFM 66.0621.01
[6] J. L. Doob, Stochastic processes, John Wiley & Sons, Inc., New York; Chapman & Hall, Limited, London, 1953. · Zbl 0053.26802
[7] P. Erdös and M. Kac, On certain limit theorems of the theory of probability, Bull. Amer. Math. Soc. 52 (1946), 292 – 302. · Zbl 0063.01274
[8] William Feller, An Introduction to Probability Theory and Its Applications. Vol. I, John Wiley & Sons, Inc., New York, N.Y., 1950. · Zbl 0077.12201
[9] T. E. Harris, First passage and recurrence distributions, Trans. Amer. Math. Soc. 73 (1952), 471 – 486. · Zbl 0048.36301
[10] Philip Hartman and Aurel Wintner, On the law of the iterated logarithm, Amer. J. Math. 63 (1941), 169 – 176. · Zbl 0024.15802
[11] E. Hopf, Ergodentheorie, Ergebnisse der Mathematik, vol. 5, no. 2, 1937. · JFM 63.0786.07
[12] A. N. Kolmogorov, Anfangsgründe der Theorie der Markoffschen Ketten mit unendlichen vielen möglichen Zuständen, Mat. Sbornik N.S. vol. 1 (1936) pp. 607-610; Bull. de l’Univ. d’Etat Moscou (in Russian) vol. 1 (1937). For an exposition in English see Chapter 1 of K. L. Chung, Lecture notes on Markov chains, Columbia Graduate Mathematical Statistics Society, New York, 1951.
[13] A. N. Kolmogorov, A local limit theorem for classical Markov chains, Izvestiya Akad. Nauk SSSR. Ser. Mat. 13 (1949), 281 – 300 (Russian).
[14] Paul Lévy, Systèmes markoviens et stationnaires. Cas dénombrable, Ann. Sci. École Norm. Sup. (3) 68 (1951), 327 – 381 (French). · Zbl 0044.33803
[15] -, Théorie de l’addition des variables aléatoires, Paris, Gauthier-Villars, 1937. · Zbl 0016.17003
[16] K. Yosida and S. Katutani, Markoff process with an enumerable infinite number of possible states, Jap. J. Math. 16 (1939), 47 – 55. · Zbl 0022.05806
[17] T. E. Harris and Herbert Robbins, Ergodic theory of Markov chains admitting an infinite invariant measure, Proc. Nat. Acad. Sci. U. S. A. 39 (1953), 860 – 864. · Zbl 0051.10503
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