David Williams FRS is a Welsh mathematician who works in

probability theory Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...

Early life and education

David Williams was born at Gorseinon, near

Swansea Swansea ( ; ) is a coastal City status in the United Kingdom, city and the List of urban areas in the United Kingdom, second-largest city of Wales. It forms a Principal areas of Wales, principal area, officially known as the City and County of ...

, Wales. He was educated at Gowerton Grammar School, winning a mathematics scholarship to Jesus College, Oxford, and went on to obtain a DPhil under the supervision of David George Kendall and Gerd Edzard Harry Reuter, with a thesis titled ''Random time substitution in Markov chains''.

Career

Williams held posts at the

Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...

(1962–63), University of Durham,

University of Cambridge The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

(1966–69), and at Swansea University (1969–85), where he was promoted to a personal chair in 1972. In 1985, he was elected to the Professorship of Mathematical Statistics, University of Cambridge, where he remained until 1992, serving as Director of the Statistical Laboratory between 1987 and 1991. Following this, he held the Chair of Mathematical Sciences jointly with the Mathematics and Statistics Groups at the

University of Bath The University of Bath is a public research university in Bath, England. Bath received its royal charter in 1966 as Bath University of Technology, along with a number of other institutions following the Robbins Report. Like the University ...

. In 1999, he returned to Swansea University, where he currently holds a Research Professorship. Williams's research interests encompass

Brownian motion Brownian motion is the random motion of particles suspended in a medium (a liquid or a gas). The traditional mathematical formulation of Brownian motion is that of the Wiener process, which is often called Brownian motion, even in mathematical ...

diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...

Markov process In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, ...

es, martingales and Wiener–Hopf theory. Recognition for his work includes being elected Fellow of the

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

in 1984, where he was cited for his achievements on the construction problem for Markov chains and on path decompositions for Brownian motion, and being awarded the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's Learned society, learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh ...

's Pólya Prize in 1994. One of his main discoveries is the decomposition of Brownian paths with respect to their maximum. He is the author of ''Probability With Martingales'' and ''Weighing the Odds'', and co-author (with L. C. G. Rogers) of both volumes of ''Diffusions, Markov Processes and Martingales''.

Books

*''Diffusions, Markov processes, and martingales'', Wiley 1979; 2nd. edn. with L. C. G. Rogers: ''Diffusions, Markov processes, and martingales, Volume One: Foundations'', Wiley 1995; reprinting of 2nd edn. Cambridge University Press 2000 *with L. C. G. Rogers: ''Diffusions, Markov processes, and martingales, Volume Two: Itō calculus'', Wiley 1988; 2nd edn. Cambridge University Press 2000 *''Probability with martingales'', Cambridge Mathematical Textbooks, Cambridge University Press 1991 *''Weighing the Odds: a course in probability and statistics'', Cambridge University Press 2001 *ed. with J. C. R. Hunt, O. M. Phillips: ''Turbulence and stochastic processes. Kolmogorov´s ideas 50 years on'', London, Royal Society 1991

References

External links

* {{DEFAULTSORT:Williams, David 20th-century Welsh mathematicians 21st-century Welsh mathematicians Academics of Durham University Academics of Swansea University Academics of the University of Bath Alumni of Jesus College, Oxford Fellows of the Royal Society Living people People educated at Gowerton Grammar School Probability theorists Professors of the University of Cambridge Stanford University Department of Mathematics faculty Year of birth missing (living people)