Donald Burkholder
Encyclopedia
Donald L. Burkholder is an American mathematician known for his contributions to probability theory
, particularly the theory of martingales
. The Burkholder–Davis–Gundy inequality is co-named after him. Donald Burkholder is a Professor Emeritus in the Department of Mathematics of the University of Illinois at Urbana-Champaign
and a CAS Professor Emeritus of Mathematics at the Center for Advanced Study, University of Illinois at Urbana-Champaign
. He is a member of the U.S. National Academy of Sciences.
, under the direction of W. Hoeffding.
He was appointed an Assistant Professor in the Department of Mathematics at the University of Illinois at Urbana-Champaign
in 1955 where he remained until his retirement in 1998. He was promoted to Associate Professor in 1960, became a Professor in the department in 1964 and was appointed as Professor at the Center for Advanced Study at UIUC in 1978.
Burkholder delivered an invited lecture at the International Congress of Mathematicians
in 1970, a Wald Lecture at the Institute of Mathematical Statistics
in 1971, a Mordell Lecture at Cambridge University in 1986, and a Zygmund Lecture at the University of Chicago
in 1988.
Donald Burkholder was elected a member of the U.S. National Academy of Sciences in 1992. The same year he was elected a fellow of the American Academy of Arts and Sciences
. On December 20, 2010 Burkholder was elected a Fellow of the American Association for the Advancement of Science
for "distinguished contributions to probability theory, particularly the theory of martingales, and his work in stochastic processes, functional analysis, and Fourier analysis."
In 2009 Burkholder was named a SIAM Fellow by the Society for Industrial and Applied Mathematics
"for advances in martingale transforms and applications of probabilistic methods in analysis".
Burkholder is a past Editor (1964–1967) of the journal Annals of Mathematical Statistics
. He served as the President of the Institute of Mathematical Statistics
in 1975-76. He is a Fellow of the Institute of Mathematical Statistics
.
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
, particularly the theory of martingales
Martingale (probability theory)
In probability theory, a martingale is a model of a fair game where no knowledge of past events can help to predict future winnings. In particular, a martingale is a sequence of random variables for which, at a particular time in the realized sequence, the expectation of the next value in the...
. The Burkholder–Davis–Gundy inequality is co-named after him. Donald Burkholder is a Professor Emeritus in the Department of Mathematics of the University of Illinois at Urbana-Champaign
University of Illinois at Urbana-Champaign
The University of Illinois at Urbana–Champaign is a large public research-intensive university in the state of Illinois, United States. It is the flagship campus of the University of Illinois system...
and a CAS Professor Emeritus of Mathematics at the Center for Advanced Study, University of Illinois at Urbana-Champaign
University of Illinois at Urbana-Champaign
The University of Illinois at Urbana–Champaign is a large public research-intensive university in the state of Illinois, United States. It is the flagship campus of the University of Illinois system...
. He is a member of the U.S. National Academy of Sciences.
Biographical data
Burkholder received a PhD in Statistics in 1955 from the University of North Carolina at Chapel HillUniversity of North Carolina at Chapel Hill
The University of North Carolina at Chapel Hill is a public research university located in Chapel Hill, North Carolina, United States...
, under the direction of W. Hoeffding.
He was appointed an Assistant Professor in the Department of Mathematics at the University of Illinois at Urbana-Champaign
University of Illinois at Urbana-Champaign
The University of Illinois at Urbana–Champaign is a large public research-intensive university in the state of Illinois, United States. It is the flagship campus of the University of Illinois system...
in 1955 where he remained until his retirement in 1998. He was promoted to Associate Professor in 1960, became a Professor in the department in 1964 and was appointed as Professor at the Center for Advanced Study at UIUC in 1978.
Burkholder delivered an invited lecture at the International Congress of Mathematicians
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
in 1970, a Wald Lecture at the Institute of Mathematical Statistics
Institute of Mathematical Statistics
The Institute of Mathematical Statistics is an international professional and scholarly society devoted to the development, dissemination, and application of statistics and probability. The Institute currently has about 4,000 members in all parts of the world...
in 1971, a Mordell Lecture at Cambridge University in 1986, and a Zygmund Lecture at the University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
in 1988.
Donald Burkholder was elected a member of the U.S. National Academy of Sciences in 1992. The same year he was elected a fellow of the American Academy of Arts and Sciences
American Academy of Arts and Sciences
The American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...
. On December 20, 2010 Burkholder was elected a Fellow of the American Association for the Advancement of Science
American Association for the Advancement of Science
The American Association for the Advancement of Science is an international non-profit organization with the stated goals of promoting cooperation among scientists, defending scientific freedom, encouraging scientific responsibility, and supporting scientific education and science outreach for the...
for "distinguished contributions to probability theory, particularly the theory of martingales, and his work in stochastic processes, functional analysis, and Fourier analysis."
In 2009 Burkholder was named a SIAM Fellow by the Society for Industrial and Applied Mathematics
Society for Industrial and Applied Mathematics
The Society for Industrial and Applied Mathematics was founded by a small group of mathematicians from academia and industry who met in Philadelphia in 1951 to start an organization whose members would meet periodically to exchange ideas about the uses of mathematics in industry. This meeting led...
"for advances in martingale transforms and applications of probabilistic methods in analysis".
Burkholder is a past Editor (1964–1967) of the journal Annals of Mathematical Statistics
Annals of Mathematical Statistics
The Annals of Mathematical Statistics was a peer-reviewed statistics journal published by the Institute of Mathematical Statistics from 1930 to 1972. It was superseded by the Annals of Statistics and the Annals of Probability.-External links:*...
. He served as the President of the Institute of Mathematical Statistics
Institute of Mathematical Statistics
The Institute of Mathematical Statistics is an international professional and scholarly society devoted to the development, dissemination, and application of statistics and probability. The Institute currently has about 4,000 members in all parts of the world...
in 1975-76. He is a Fellow of the Institute of Mathematical Statistics
Institute of Mathematical Statistics
The Institute of Mathematical Statistics is an international professional and scholarly society devoted to the development, dissemination, and application of statistics and probability. The Institute currently has about 4,000 members in all parts of the world...
.
Selected publications
- Burkholder, D. L.; Gundy, Richard F., Extrapolation and interpolation of quasi-linear operators on martingales. Acta MathematicaActa MathematicaActa Mathematica is a journal publishing original research papers in all fields of mathematics. The journal was founded by Gösta Mittag-Leffler in 1882 and is published by Institut Mittag-Leffler, a research institute for mathematics belonging to the Royal Swedish Academy of Sciences...
, vol. 124 (1970), pp. 249–304 - Burkholder, Donald L., Inequalities for operators on martingales. Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 2, pp. 551–557. Gauthier-Villars, Paris, 1971.
- Burkholder, Donald L., Distribution function inequalities for martingales, Annals of Probability, vol. 1 (1973), pp. 19–42
- Burkholder, Donald L., A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional. Annals of Probability, vol. 9 (1981), no. 6, pp. 997–1011
- Burkholder, Donald L., Explorations in martingale theory and its applications. École d'Été de Probabilités de Saint-Flour XIX-1989, pp. 1–66, Lecture Notes in Mathematics, vol. 1464, Springer-Verlag, Berlin, 1991
See also
- MartingalesMartingale (probability theory)In probability theory, a martingale is a model of a fair game where no knowledge of past events can help to predict future winnings. In particular, a martingale is a sequence of random variables for which, at a particular time in the realized sequence, the expectation of the next value in the...
- Burkholder–Davis–Gundy inequality
External links
- Burkholder's personal web page, Department of Mathematics, University of Illinois at Urbana-ChampaignUniversity of Illinois at Urbana-ChampaignThe University of Illinois at Urbana–Champaign is a large public research-intensive university in the state of Illinois, United States. It is the flagship campus of the University of Illinois system...
- Donald L. Burkholder, CAS Professor Emeritus of Mathematics, Center for Advanced Study, University of Illinois at Urbana-ChampaignUniversity of Illinois at Urbana-ChampaignThe University of Illinois at Urbana–Champaign is a large public research-intensive university in the state of Illinois, United States. It is the flagship campus of the University of Illinois system...
- Donald Burkholder at the Mathematics Genealogy ProjectMathematics Genealogy ProjectThe Mathematics Genealogy Project is a web-based database for the academic genealogy of mathematicians. As of September, 2010, it contained information on approximately 145,000 mathematical scientists who contribute to "research-level mathematics"...