Some new developments in Markov chains

Some new developments in Markov chains
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by K. L. Chung

Trans. Amer. Math. Soc. 81 (1956), 195-210

DOI: https://doi.org/10.1090/S0002-9947-1956-0075481-4

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References

Donald G. Austin, On the existence of the derivative of Markoff transition probability functions, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 224–226. MR 70095, DOI 10.1073/pnas.41.4.224
K. L. Chung, Foundations of the theory of continuous parameter Markov chains, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–1955, vol. II, University of California Press, Berkeley-Los Angeles, Calif., 1956, pp. 29–40. MR 0084884
J. L. Doob, Topics in the theory of Markoff chains, Trans. Amer. Math. Soc. 52 (1942), 37–64. MR 6633, DOI 10.1090/S0002-9947-1942-0006633-7
J. L. Doob, Markoff chains—denumerable case, Trans. Amer. Math. Soc. 58 (1945), 455–473. MR 13857, DOI 10.1090/S0002-9947-1945-0013857-4
J. L. Doob, Renewal theory from the point of view of the theory of probability, Trans. Amer. Math. Soc. 63 (1948), 422–438. MR 25098, DOI 10.1090/S0002-9947-1948-0025098-8

Stochastic processes

A. N. Kolmogorov, On the differentiability of the transition probabilities in stationary Markov processes with a denumberable number of states, Moskov. Gos. Univ. Učenye Zapiski Matematika 148(4) (1951), 53–59 (Russian). MR 0050210
Paul Lévy, Systèmes markoviens et stationnaires. Cas dénombrable, Ann. Sci. École Norm. Sup. (3) 68 (1951), 327–381 (French). MR 0047961