Celebratio Mathematica

J. L. Doob: “Time series and harmonic analysis,” pp. 303–343 in Proceedings of the Berkeley symposium on mathematical statistics and probability (Berkeley, CA, 13–18 August 1945 and 27–29 January 1946). Edited by J. Neyman. University of California Press (Berkeley and Los Angeles), 1949. MR 27979 Zbl 0038.29902 incollection

Although many articles on the present subject have appeared in the mathematical, statistical, and physical literature, there still seems to be some justification for one more. The statisticians have applied only small parts of the theory; the physicists have gone deeper, but write like physicists; the mathematicians have gone furthest, but write like mathematicians, only for posterity. Their work is frequently not understood, and is in general either ignored or applied in simplified forms which often are formally more formidable than the original rigorous one. The present paper attempts to give a compact outline of the harmonic analysis of stochastic processes, with applications to physical problems.

J. L. Doob: “Continuous parameter martingales,” pp. 269–277 in Proceedings of the second Berkeley symposium on mathematical statistics and probability (Berkeley, CA, 31 July–12 August 1950). Edited by J. Neyman. University of California Press (Berkeley and Los Angeles), 1951. MR 44770 Zbl 0044.33802 incollection

J. L. Doob: “Probability methods applied to the first boundary value problem,” pp. 49–80 in Proceedings of the third Berkeley symposium on mathematical statistics and probability (Berkeley, CA, 26–31 December 1954 and July–August 1955), vol. 2: Contributions to probability theory. Edited by J. Neyman. University of California Press (Berkeley and Los Angeles), 1956. MR 84886 Zbl 0074.09101 incollection

J. L. Doob: “Appreciation of Khinchin,” pp. 17–20 in Proceedings of the fourth Berkeley symposium on mathematical statistics and probability (Berkeley, CA, 20 June–30 July 1960), vol. 2. Edited by J. Neyman. University of California Press (Berkeley, CA), 1961. MR 131342 incollection

Jerzy Neyman	Related
Aleksandr Yakovlevich Khinchin	Related

J. L. Doob: “Notes on martingale theory,” pp. 95–102 in Proceedings of the fourth Berkeley symposium on mathematical statistics and probability (Berkeley, CA, 20 June–30 July 1960), vol. 2. Edited by J. Neyman. University of California Press (Berkeley, CA), 1961. MR 133182 Zbl 0126.14003 incollection

Although several writers, for example Bernstein, Lévy, and Ville, had used what would now be identified as martingale concepts, the first systematic studies appeared in [Doob 1940, 1953]. Since then, martingale theory has been applied extensively, but little progress has been made in the theory itself. The purpose of hte present paper is to point out how much spade work remains to be done in the theory, by deriving new theorems without the use of deep technical apparatus.

Throughout this paper, the more appropriate nomenclature “submartingale,”, “supermartingale” is used, rather than the “semimartingale” found in [1953]. The unifying thread in the following work will be the fact that certain simple operations on submartingales transform them into submartingales. This leads to a new submartingale convergence theorem, to a sharpening of the upcrossing inequality, and thereby into an examination of apparently hitherto unnoticed interrelations between martingale and potential theory.

J. L. Doob: “William Feller and twentieth century probability,” pp. xv–xx in Proceedings of the sixth Berkeley symposium on mathematical statistics and probability (Berkeley, CA, 21 June–18 July 1970), vol. 2: Probability theory. Edited by L. M. Le Cam, J. Neyman, and E. L. Scott. University of California Press (Berkeley, CA), 1972. MR 386946 Zbl 0251.01009 incollection

William Feller	Related
Elizabeth Leonard Scott	Related
Jerzy Neyman	Related
Lucien Marie Le Cam	Related

J. L. Doob: “The structure of a Markov chain,” pp. 131–141 in Proceedings of the sixth Berkeley symposium on mathematical statistics and probability (Berkeley, CA, 21 June–18 July 1970), vol. 3: Probability theory. Edited by L. M. Le Cam, J. Neyman, and E. L. Scott. University of California Press (Berkeley, CA), 1972. MR 405603 Zbl 0255.60042 incollection

Lucien Marie Le Cam	Related
Elizabeth Leonard Scott	Related
Jerzy Neyman	Related

J. L. Doob: “Analytic sets and stochastic processes,” pp. 1–12 in Stochastic processes and related topics (Bloomington, IN, 31 July–9 August 1974), vol. 1. Edited by M. L. Puri. Academic Press (New York), 1975. Book dedicated to Jerzy Neyman. MR 380959 Zbl 0322.60006 incollection

Madan Lal Puri	Related
Jerzy Neyman	Related

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