Contributions to the theory of Markov chains. II
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References
- Kai Lai Chung, Contributions to the theory of Markov chains, J. Research Nat. Bur. Standards 50 (1953), 203–208. MR 0055608
- K. L. Chung and W. H. J. Fuchs, On the distribution of values of sums of random variables, Mem. Amer. Math. Soc. 6 (1951), 12. MR 40610
- Wolfgang Doeblin, Sur deux problèmes de M. Kolmogoroff concernant les chaînes dénombrables, Bull. Soc. Math. France 66 (1938), 210–220 (French). MR 1505091 —, Thèse, Paris (printed in Bucharest), 1938.
- J. L. Doob, The law of large numbers for continuous stochastic processes, Duke Math. J. 6 (1940), 290–306. MR 2053
- J. L. Doob, Stochastic processes, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1953. MR 0058896
- P. Erdös and M. Kac, On certain limit theorems of the theory of probability, Bull. Amer. Math. Soc. 52 (1946), 292–302. MR 15705, DOI 10.1090/S0002-9904-1946-08560-2
- William Feller, An Introduction to Probability Theory and Its Applications. Vol. I, John Wiley & Sons, Inc., New York, N.Y., 1950. MR 0038583
- T. E. Harris, First passage and recurrence distributions, Trans. Amer. Math. Soc. 73 (1952), 471–486. MR 52057, DOI 10.1090/S0002-9947-1952-0052057-2
- Philip Hartman and Aurel Wintner, On the law of the iterated logarithm, Amer. J. Math. 63 (1941), 169–176. MR 3497, DOI 10.2307/2371287 E. Hopf, Ergodentheorie, Ergebnisse der Mathematik, vol. 5, no. 2, 1937. 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.
- A. N. Kolmogorov, A local limit theorem for classical Markov chains, Izvestiya Akad. Nauk SSSR. Ser. Mat. 13 (1949), 281–300 (Russian). MR 0031216
- Paul Lévy, Systèmes markoviens et stationnaires. Cas dénombrable, Ann. Sci. École Norm. Sup. (3) 68 (1951), 327–381 (French). MR 0047961 —, Théorie de l’addition des variables aléatoires, Paris, Gauthier-Villars, 1937.
- K. Yosida and S. Katutani, Markoff process with an enumerable infinite number of possible states, Jpn. J. Math. 16 (1939), 47–55. MR 375, DOI 10.4099/jjm1924.16.0_{4}7
- 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. MR 56873, DOI 10.1073/pnas.39.8.860
Additional Information
- © Copyright 1954 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 76 (1954), 397-419
- MSC: Primary 60.0X
- DOI: https://doi.org/10.1090/S0002-9947-1954-0063603-9
- MathSciNet review: 0063603