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==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 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.


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 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.


==Results==
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.


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]].  
Doob's approach to probability was evident in his first probability paper: ''Probability and Statistics'', Transactions of the AMS, 1934. In this paper 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.


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]]).  
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 what is known about the various types of Stochastic Processes.  So he wrote such a book called "Stochastic Processes." It was published in 1953 soon became one of the most influential books in the development of probability theory.


Feller initiated the publication of the now well-known review journal ''[[Mathematical Reviews]]''.
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.  The first half of this book dealt 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 are really pretty much the same.


==External links==
==Honors==
 
Doob Honors
 
President of the Institute of Mathematical Statistics in 1950.<br>
 
President of the American Mathematical Society 1963-1964.<br>
 
Elected to American Academy of the Arts and Sciences 1965.<br>
 
Associate of the French Academy of Sciences 1975.<br>
 
Awarded the National Medal of Science by President Carter 1979.<br>


*[http://jagor.srce.hr/zuh/velikani/vel_int.htm Croatian Giants of Science - in Croatian]
Awarded the Steele Prize by the American Mathematical Society. 1984<br>
*[http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Feller.html MacTutor: William Feller]


[[Category:1906 births|Feller, William]][[Category:1970 deaths|Feller, William]]
==External links==
[[Category:American mathematicians|Feller, William]]
[[Category:Croatian mathematicians|Feller, William]]
[[Category:20th century mathematicians|Feller, William]]


[[de:William Feller]]
*[http://www.dartmouth.edu/~chance/Doob/conversation.html A Conversation with Joe Doob]
*[http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Doob.html Doob biography]
*[http://www.math.uiuc.edu/People/doob_record.html Record of the Celebration of the Life of Joseph Leo Doob]

Latest revision as of 13:00, 9 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 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: Probability and Statistics, Transactions of the AMS, 1934. In this paper 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.

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 what is known about the various types of Stochastic Processes. So he wrote such a book called "Stochastic Processes." It was published in 1953 soon became one of the most influential books in the development of 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. The first half of this book dealt 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 are really pretty much the same.

Honors

Doob Honors

President of the Institute of Mathematical Statistics in 1950.

President of the American Mathematical Society 1963-1964.

Elected to American Academy of the Arts and Sciences 1965.

Associate of the French Academy of Sciences 1975.

Awarded the National Medal of Science by President Carter 1979.

Awarded the Steele Prize by the American Mathematical Society. 1984

External links