Difference between revisions of "Main Page/doob"

From ChanceWiki
Jump to navigation Jump to search
Line 7: Line 7:
 
==Work==
 
==Work==
  
The works of Feller are contained in 104 papers and two books on a variety of topics such as [[mathematical analysis]], theory of [[measurement]], [[functional analysis]], [[geometry]], and [[differential equations]].
+
Doob's thesis was on boundary values of analytic functions. He published two papers based on his 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.
  
He was the foremost [[list of probabilists | probabilist]] outside of [[Russia]]. In the middle of the [[20th century]], [[probability theory|probability]] was not generally viewed as a fruitful area of [[research]] in mathematics except in [[Russia]], where [[Kolmogorov]] and others were influential. Feller contributed to the study of the relationship between [[Markov chain]]s and [[differential equation]]s. He wrote a two-volume treatise on [[probability theory|probability]] that has since been universally regarded as one of the most important treatments of that subject.
+
The Great Depression of 1929 was still going strong in the thirties and Doob could not find a job. B.O. Koopman  at Columbia 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: expected value for integral, random variable for function, event for subset etc. 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: ''Probability and Statistics'', Transactions of the AMS, 1934. Doob proved theorems related to the law of large numbers, using the fact that the law of large numbers follows from 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.
  
 
==Results==
 
==Results==

Revision as of 14:36, 8 November 2005

Joeseph Leonard Doob February 27 1910 - June 27 2004.

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 "under-achieving" 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.

Work

Doob's thesis was on boundary values of analytic functions. He published two papers based on his 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 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: expected value for integral, random variable for function, event for subset etc. 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: Probability and Statistics, Transactions of the AMS, 1934. Doob proved theorems related to the law of large numbers, using the fact that the law of large numbers follows from 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.

Results

Numerous topics relating to probability are named after him as Feller process, Feller explosion test, Feller-Brown movement, Feller property, Lindberg-Feller theorem. Books written by him and published as the textbooks are being considered invaluable in popularisation of the theory of probability and the best written during the 20th century.

Despite the fact that he spent the better part of his life out of Croatia where he was born and grew up, and where he started his education, he was in touch with relatives and the colleagues at University of Zagreb whom he often visited, and where he frequently lectured. He received numerous awards and was an honoured member of numerous educational institution (Boston, Zagreb, London, Copenhagen).

Feller initiated the publication of the now well-known review journal Mathematical Reviews.

External links

de:William Feller