×

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


PDFBibTeX XMLCite
Full Text: DOI

References:

[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 · doi:10.2307/2371287
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.