Joseph L. Doob
Joseph L. Doob | |
---|---|
PhD) | |
Known for | Doob's martingale inequality University of Illinois at Urbana-Champaign |
Doctoral advisor | Joseph L. Walsh |
Doctoral students |
Joseph Leo Doob (February 27, 1910 – June 7, 2004) was an American mathematician, specializing in analysis and probability theory.
The theory of martingales was developed by Doob.
Early life and education
Doob was born in
Work
Doob's thesis was on boundary values of analytic functions. He published two papers based on this thesis, which appeared in 1932 and 1933 in the Transactions of the American Mathematical Society. Doob returned to this subject many years later when he proved a probabilistic version of Fatou's boundary limit theorem for harmonic functions.
The
In 1933
Doob's approach to probability was evident in his first probability paper,
After writing a series of papers on the foundations of probability and stochastic processes including
Beyond this book, Doob is best known for his work on martingales and probabilistic potential theory. After he retired, Doob wrote a book of over 800 pages: Classical Potential Theory and Its Probabilistic Counterpart.[4] The first half of this book deals with classical potential theory and the second half with probability theory, especially martingale theory. In writing this book, Doob shows that his two favorite subjects, martingales and potential theory, can be studied by the same mathematical tools.
The
Honors
- President of the Institute of Mathematical Statistics in 1950.
- Elected to National Academy of Sciences 1957.
- President of the American Mathematical Society 1963–1964.
- Elected to American Academy of Arts and Sciences 1965.
- Associate of the French Academy of Sciences 1975.
- Awarded the National Medal of Science by the President of the United States Jimmy Carter 1979.[6]
- Awarded the Steele Prizeby the American Mathematical Society. 1984.
Publications
- Books
- — (1953). Stochastic Processes. ISBN 0-471-52369-0.[7]
- — (1984). Classical Potential Theory and Its Probabilistic Counterpart. Berlin Heidelberg New York: ISBN 3-540-41206-9.[8]
- — (1993). Measure Theory. Berlin Heidelberg New York: Springer-Verlag.[9]
- Articles
- Joseph Leo Doob (1 June 1934). "Stochastic Processes and Statistics". Wikidata Q33740310.
- — (1934). "Probability and statistics". JSTOR 1989822.
- — (1957). "Conditional brownian motion and the boundary limits of harmonic functions" (PDF). Bulletin de la Société Mathématique de France. 85: 431–458. .
- — (1959). "A non probabilistic proof of the relative Fatou theorem" (PDF). Annales de l'Institut Fourier. 9: 293–300. doi:10.5802/aif.93.
- — (1962). "Boundary properties of functions with finite Dirichlet integrals" (PDF). Annales de l'Institut Fourier. 12: 573–621. doi:10.5802/aif.126.
- — (1963). "Limites angulaires et limites fines" (PDF). Annales de l'Institut Fourier. 13 (2): 395–415. doi:10.5802/aif.152.
- — (1965). "Some classical function theory theorems and their modern versions" (PDF). Annales de l'Institut Fourier. 15 (1): 113–135. doi:10.5802/aif.200.
- — (1967). "Erratum: Some classical function theory theorems and their modern versions" (PDF). Annales de l'Institut Fourier. 17 (1): 469. doi:10.5802/aif.264.
- — (1973). "Boundary approach filters for analytic functions" (PDF). Annales de l'Institut Fourier. 23 (3): 187–213. doi:10.5802/aif.476.
- — (1975). "Stochastic process measurability conditions" (PDF). Annales de l'Institut Fourier. 25 (3–4): 163–176. doi:10.5802/aif.577.
See also
- Martingale (probability theory)
- Doob–Dynkin lemma
- Doob martingale
- Doob's martingale convergence theorems
- Doob's martingale inequality
- Doob–Meyer decomposition theorem
- Optional stopping theorem
Notes
- ^ Doob, Joseph Leo, Community of Scholars Profile, IAS Archived 2013-10-10 at the Wayback Machine
- ^ J.L. Doob Probability and statistics
- ^ Doob J.L., Stochastic Processes
- ^ Doob J.L., Classical Potential Theory and Its Probabilistic Counterpart
- ^ Joseph L. Doob Prize. American Mathematical Society. Accessed September 1, 2008
- ^ National Science Foundation – The President's National Medal of Science
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