Celebratio Mathematica — Chung

Markov chains

Works connected to Jerzy Neyman

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K. L. Chung: “Foundations of the theory of continuous parameter Markov chains,” pp. 29–40 in Proceedings of the third Berkeley symposium on mathematical statistics and probability, 1954–1955, vol. II: Contributions to probability theory. Edited by J. Neyman. University of California Press (Berkeley, CA and Los Angeles, CA), 1956. MR 0084884 Zbl 0071.35001 inproceedings

This paper is exclusively concerned with continuous parameter Markov processes with a denumerably infinite number of states and stationary transition matrix function. The foundations of the proper theory of such processes, as distinguished from that of the discrete parameter version, or of Markov processes which are either more special (for example, general state space; nonstationary transition matrix function), were laid by Doob [1942; 1945], and Lévy [1951; 1952; 1953]. Roughly speaking it was Lévy in 1952 who drew, in his inimitable way, the comprehensive picture while Doob, ten years earlier, had supplied the essential ingredients. The present effor aims at a synthesis of the most fundamental parts of the theory, made possible by the contributions of these two authors. While the results given here generally extend and clarify those in the cited literature, immense credit must go to Professors Lévy and Doob for the inspiration of their pioneer work. To them I am also indebted for much valuable discussion through correspondence and conversation. An attempt is made in the presentation to be quite formal and rigorous, in the spirit of Doob’s already classic treatise [1953]. Further developments of the theory will be published elsewhere.

K. L. Chung: “Probabilistic methods in Markov chains,” pp. 35–56 in Proceedings of the fourth Berkeley symposium on mathematical statistics and probability, vol. II. Edited by J. Neyman. University of California Press (Berkeley, CA), 1961. MR 0131901 Zbl 0106.33303 incollection