Joseph L. Doob | |
|---|---|
 Doob in Tokyo, 1969 | |
| Born | (1910-02-27)February 27, 1910 |
| Died | June 7, 2004(2004-06-07) (aged 94) |
| Alma mater | Harvard University (BA,MA,PhD) |
| Known for | Doob's martingale inequality Doob decomposition theorem |
| Scientific career | |
| Fields | Mathematics |
| Institutions | 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 inanalysis andprobability theory.
The theory ofmartingales was developed by Doob.
Doob was born inCincinnati, Ohio, February 27, 1910, the son of a Jewish couple, Leo Doob and Mollie Doerfler Doob. The family moved toNew York City before he was three years old. The parents felt that he was underachieving in grade school and placed him in theEthical Culture School, from which he graduated in 1926. He then went on toHarvard where he received a BA in 1930, an MA in 1931, and a PhD (Boundary Values of Analytic Functions, advisorJoseph L. Walsh) in 1932. After postdoctoral research atColumbia andPrinceton, he joined the department of mathematics of theUniversity 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 theInstitute for Advanced Study for the academic year 1941–1942[1] whenOswald Veblen approached him to work on mine warfare for the Navy.
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 ofFatou's boundary limit theorem for harmonic functions.
TheGreat 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 statisticianHarold Hotelling might have a grant that would permit Doob to work with him. Hotelling did, so the Depression led Doob to probability.
In 1933Kolmogorov 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 becamemeasure 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 thelaw of large numbers, using a probabilistic interpretation ofBirkhoff's ergodic theorem. Then he used these theorems to give rigorous proofs of theorems proven byFisher and Hotelling related to Fisher'smaximum likelihood estimator for estimating a parameter of a distribution.
After writing a series of papers on the foundations of probability and stochastic processes includingmartingales,Markov processes, andstationary processes, Doob realized that there was a real need for a book showing what is known about the various types ofstochastic processes, so he wrote the bookStochastic Processes.[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 onmartingales and probabilisticpotential 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 withprobability 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.
TheAmerican Mathematical Society'sJoseph L. Doob Prize, endowed in 2005 and awarded every three years for an outstanding mathematical book, is named in Doob's honor.[5] The postdoctoral members of the department of mathematics of theUniversity of Illinois are named J L Doob Research Assistant Professors.
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