The Annals of Probability

J. L. Doob: Foundations of stochastic processes and probabilistic potential theory

Ronald Getoor

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Abstract

During the three decades from 1930 to 1960 J. L. Doob was, with the possible exception of Kolmogorov, the man most responsible for the transformation of the study of probability to a mathematical discipline. His accomplishments were recognized by both probabilists and other mathematicians in that he is the only person ever elected to serve as president of both the IMS and the AMS. This article is an attempt to discuss his contributions to two areas in which his work was seminal, namely, the foundations of continuous parameter stochastic processes and probabilistic potential theory.

Article information

Source
Ann. Probab., Volume 37, Number 5 (2009), 1647-1663.

Dates
First available in Project Euclid: 21 September 2009

Permanent link to this document
https://projecteuclid.org/euclid.aop/1253539851

Digital Object Identifier
doi:10.1214/09-AOP465

Mathematical Reviews number (MathSciNet)
MR2561428

Zentralblatt MATH identifier
1176.60026

Subjects
Primary: 60G05: Foundations of stochastic processes 60J45: Probabilistic potential theory [See also 31Cxx, 31D05]

Keywords
Doob continuous parameter processes probabilistic potential theory

Citation

Getoor, Ronald. J. L. Doob: Foundations of stochastic processes and probabilistic potential theory. Ann. Probab. 37 (2009), no. 5, 1647--1663. doi:10.1214/09-AOP465. https://projecteuclid.org/euclid.aop/1253539851


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References

  • [B] Bingham, N. H. (2005). Doob: A half-century on. J. Appl. Probab. 42 257–266.
  • [BP] Burkholder, D. and Protter, P. (2005). Joseph Leo Doob, 1910–2004. Stochastic Process. Appl. 115 1061–1072.
  • [DY] Dynkin, E. and Jushkevich, A. (1956). Strong Markov processes. Teor. Veroyatnost. i Primenen. 1 149–155.
  • [H] Hunt, G. A. (1956). Some theorems concerning Brownian motion. Trans. Amer. Math. Soc. 81 294–319.
  • [K] Kakutani, S. (1944). Two-dimensional Brownian motion and harmonic functions. Proc. Imp. Acad. Tokyo 20 706–714.
  • [M1] Meyer, P.-A. (1966). Probability and Potentials. Blaisdell, Boston.
  • [M2] Meyer, P.-A. (1968). La théorie générale des processus de Markov à temps continu. Unpublished manuscript.
  • [M3] Meyer, P.-A. (2000). Les processus stochastiques de 1950 à nos jours. In Development of Mathematics 19502000 ( J. P. Pier, ed.) 813–848. Birkhäuser, Basel.
  • [Sh] Sharpe, M. J. (1986). S. Kakutani’s work on Brownian motion. In Contemporary Mathematicians—Selected Works of S. Kakutani (R. Kallman, ed.) 2 397–401. Birkhäuser, Basel.
  • [Sn] Snell, J. L. (1997). A conversation with Joe Doob. Statist. Sci. 12 301–311.