Joseph L. Doob
Joseph L. "Joe" Doob  

Tokyo, 1969 (courtesy MFO)


Born  Cincinnati, Ohio, U.S. 
February 27, 1910
Died  Script error: The function "death_date_and_age" does not exist. Urbana, Illinois, U.S. 
Residence  U.S. 
Nationality  American 
Fields  Mathematician 
Institutions  University of Illinois at UrbanaChampaign 
Alma mater  Harvard University 
Doctoral advisor  Joseph L. Walsh 
Doctoral students  Warren Ambrose David Blackwell YuanShih Chow Paul Halmos J. Laurie Snell 
Known for  Doob martingale 
Joseph Leo "Joe" 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.
Contents
Early life and education
Doob was born in Cincinnati, Ohio, February 27, 1910, the son of Leo Doob and Mollie Doerfler Doob. The family moved to New York City before he was three years old. The parents felt that he was underachieving in grade school and placed him in the Ethical Culture School, from which he graduated in 1926. He then went on to Harvard where he received a BA in 1930, an MA in 1931, and a PhD in 1932. After postdoctoral research at Columbia and Princeton, he joined the Department of Mathematics of the University of Illinois in 1935 and served until his retirement in 1978. He was a member of the Urbana campus's Center for Advanced Study from its beginning in 1959. During the Second World War, he worked in Washington, D. C. and Guam as a civilian consultant to the Navy from 1942 to 1945; he was at the Institute for Advanced Study for the academic year 1941–1942 ^{[1]} when Oswald Veblen approached him to work on mine warfare for the Navy.
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 AMS. Doob returned to this subject many years later when he proved a probabilistic version of Fatou's boundary limit theorem for harmonic functions.
The Great Depression of 1929 was still going strong in the thirties and Doob could not find a job. B.O. Koopman at Columbia University suggested that statistician Harold Hotelling might have a grant that would permit Doob to work with him. Hotelling did, so the Depression led Doob to probability.
In 1933 Kolmogorov provided the first axiomatic foundation for the theory of probability. Thus a subject that had originated from intuitive ideas suggested by real life experiences and studied informally, suddenly became mathematics. Probability theory became measure theory with its own problems and terminology. Doob recognized that this would make it possible to give rigorous proofs for existing probability results, and he felt that the tools of measure theory would lead to new probability results.
Doob's approach to probability was evident in his first probability paper,^{[2]} in which he proved theorems related to the law of large numbers, using a probabilistic interpretation of Birkhoff's ergodic theorem. Then he used these theorems to give rigorous proofs of theorems proven by Fisher and Hotelling related to Fisher's maximum likelihood estimator for estimating a parameter of a distribution.
After writing a series of papers on the foundations of probability and stochastic processes including martingales, Markov processes, and stationary processes, Doob realized that there was a real need for a book showing what is known about the various types of stochastic processes. So he wrote his famous "Stochastic Processes" book.^{[3]} It was published in 1953 and soon became one of the most influential books in the development of modern probability theory.
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 American Mathematical Society's Joseph L. Doob Prize, endowed in 2005 and awarded every three years for an outstanding mathematical book, is named in Doob's honor.^{[5]}
Honors
 President of the Institute of Mathematical Statistics in 1950.
 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 Prize by the American Mathematical Society. 1984.
See also
 Martingale (probability theory)
 Doob–Dynkin lemma
 Doob martingale
 Doob's martingale convergence theorems
 Doob's martingale inequality
 Doob–Meyer decomposition theorem
Notes
 ↑ Doob, Joseph Leo, Community of Scholars Profile, IAS
 ↑ 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
References
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External links
 Joseph L. Doob at the Mathematics Genealogy Project
 A Conversation with Joe Doob
 Doob biography
 Record of the Celebration of the Life of Joseph Leo Doob
 Articles by Doob
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 1910 births
 2004 deaths
 20thcentury American mathematicians
 21stcentury American mathematicians
 Columbia University staff
 Harvard University alumni
 Institute for Advanced Study visiting scholars
 Mathematical analysts
 Members of the French Academy of Sciences
 National Medal of Science laureates
 People from Cincinnati, Ohio
 Presidents of the American Mathematical Society
 Presidents of the Institute of Mathematical Statistics
 Princeton University staff
 Probability theorists
 Researchers in stochastics
 University of Illinois at Urbana–Champaign faculty