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Joseph L. Doob

January 01, 1970

Joseph Leo Doob (February 27, 1910 – June 7, 2004) was an American mathematician, specializing in analysis and probability theory.

Joseph L. Doob
Doob in Tokyo, 1969
Born(1910-02-27)February 27, 1910
Cincinnati, Ohio, U.S.
DiedJune 7, 2004(2004-06-07) (aged 94)
Urbana, Illinois, U.S.
NationalityAmerican
Alma materHarvard University (BA, MA, PhD)
Known forDoob's martingale inequality
Doob decomposition theorem
Scientific career
FieldsMathematics
InstitutionsUniversity of Illinois at Urbana-Champaign
Doctoral advisorJoseph L. Walsh
Doctoral students

The theory of martingales was developed by Doob.

Early life and education edit

Doob was born in Cincinnati, Ohio, February 27, 1910, the son of a Jewish couple, 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 (Boundary Values of Analytic Functions, advisor Joseph L. Walsh) 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 edit

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 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 the book Stochastic 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 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] The postdoctoral members of the department of mathematics of the University of Illinois are named J L Doob Research Assistant Professors.

Honors edit

Publications edit

Books
  • — (1953). Stochastic Processes. John Wiley & Sons. ISBN 0-471-52369-0.[7]
  • — (1984). Classical Potential Theory and Its Probabilistic Counterpart. Berlin Heidelberg New York: Springer-Verlag. 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". Proceedings of the National Academy of Sciences of the United States of America. 20 (6): 376–379. Bibcode:1934PNAS...20..376D. doi:10.1073/PNAS.20.6.376. ISSN 0027-8424. PMC 1076423. PMID 16587907. Zbl 0009.22101. Wikidata Q33740310.
  • — (1934). "Probability and statistics". Transactions of the American Mathematical Society. 36 (4). American Mathematical Society: 759–775. doi:10.2307/1989822. JSTOR 1989822.
  • — (1957). "Conditional brownian motion and the boundary limits of harmonic functions" (PDF). Bulletin de la Société Mathématique de France. 85: 431–458. doi:10.24033/bsmf.1494.
  • — (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 edit

Notes edit

  1. ^ Doob, Joseph Leo, Community of Scholars Profile, IAS 2013-10-10 at the Wayback Machine
  2. ^ J.L. Doob Probability and statistics
  3. ^ Doob J.L., Stochastic Processes
  4. ^ Doob J.L., Classical Potential Theory and Its Probabilistic Counterpart
  5. ^ Joseph L. Doob Prize. American Mathematical Society. Accessed September 1, 2008
  6. ^ National Science Foundation – The President's National Medal of Science
  7. ^ Chung, K. L. (1954). "Review of Stochastic processes by J. L. Doob". Bull. Amer. Math. Soc. 60: 190–201. doi:10.1090/S0002-9904-1954-09801-4.
  8. ^ Meyer, P. A. (1985). "Review of Classical potential theory and its probabilistic counterpart by J. L. Doob". Bull. Amer. Math. Soc. (N.S.). 12: 177–181. doi:10.1090/S0273-0979-1985-15340-6.
  9. ^ Meyer, P. A. (1994). "Review of Measure theory by J. L. Doob". Bull. Amer. Math. Soc. (N.S.). 31: 233–235. doi:10.1090/S0273-0979-1994-00541-5.

External links edit

January 01, 1970
joseph, doob, joseph, doob, february, 1910, june, 2004, american, mathematician, specializing, analysis, probability, theory, doob, tokyo, 1969born, 1910, february, 1910cincinnati, ohio, diedjune, 2004, 2004, aged, urbana, illinois, nationalityamericanalma, ma. Joseph Leo Doob February 27 1910 June 7 2004 was an American mathematician specializing in analysis and probability theory Joseph L DoobDoob in Tokyo 1969Born 1910 02 27 February 27 1910Cincinnati Ohio U S DiedJune 7 2004 2004 06 07 aged 94 Urbana Illinois U S NationalityAmericanAlma materHarvard University BA MA PhD Known forDoob s martingale inequality Doob decomposition theoremScientific careerFieldsMathematicsInstitutionsUniversity of Illinois at Urbana ChampaignDoctoral advisorJoseph L WalshDoctoral studentsWarren Ambrose David Blackwell Yuan Shih Chow Paul Halmos J Laurie Snell Mary E Thompson The theory of martingales was developed by Doob Contents 1 Early life and education 2 Work 3 Honors 4 Publications 5 See also 6 Notes 7 External linksEarly life and education editDoob was born in Cincinnati Ohio February 27 1910 the son of a Jewish couple 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 Boundary Values of Analytic Functions advisor Joseph L Walsh 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 editDoob 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 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 the book Stochastic 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 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 The postdoctoral members of the department of mathematics of the University of Illinois are named J L Doob Research Assistant Professors Honors editPresident 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 Prize by the American Mathematical Society 1984 Publications editBooks 1953 Stochastic Processes John Wiley amp Sons ISBN 0 471 52369 0 7 1984 Classical Potential Theory and Its Probabilistic Counterpart Berlin Heidelberg New York Springer Verlag 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 Proceedings of the National Academy of Sciences of the United States of America 20 6 376 379 Bibcode 1934PNAS 20 376D doi 10 1073 PNAS 20 6 376 ISSN 0027 8424 PMC 1076423 PMID 16587907 Zbl 0009 22101 Wikidata Q33740310 1934 Probability and statistics Transactions of the American Mathematical Society 36 4 American Mathematical Society 759 775 doi 10 2307 1989822 JSTOR 1989822 1957 Conditional brownian motion and the boundary limits of harmonic functions PDF Bulletin de la Societe Mathematique de France 85 431 458 doi 10 24033 bsmf 1494 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 editMartingale probability theory Doob Dynkin lemma Doob martingale Doob s martingale convergence theorems Doob s martingale inequality Doob Meyer decomposition theorem Optional stopping theoremNotes edit 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 Chung K L 1954 Review of Stochastic processes by J L Doob Bull Amer Math Soc 60 190 201 doi 10 1090 S0002 9904 1954 09801 4 Meyer P A 1985 Review of Classical potential theory and its probabilistic counterpart by J L Doob Bull Amer Math Soc N S 12 177 181 doi 10 1090 S0273 0979 1985 15340 6 Meyer P A 1994 Review of Measure theory by J L Doob Bull Amer Math Soc N S 31 233 235 doi 10 1090 S0273 0979 1994 00541 5 External links editJoseph L Doob at the Mathematics Genealogy Project A Conversation with Joe Doob Archived 2018 06 22 at the Wayback Machine Doob biography Record of the Celebration of the Life of Joseph Leo Doob Retrieved from https en wikipedia org w index php title Joseph L Doob amp oldid 1222490333, wikipedia, wiki, book, books, library,

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