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Williams's research interests encompass Brownian motion, diffusions, Markov processes, martingales and Wiener–Hopf theory. Recognition for his work includes being elected Fellow of the Royal Society in 1984, where he was cited for his achievements on the construction problem for Markov chains and on path decompositions for Brownian motion ...
Chan, Terence (1996), "Some diffusion models for the Mabinogion sheep problem of Williams", Advances in Applied Probability, 28 (3): 763– 783, doi:10.2307/1428180, MR 1404309 Williams, David (1991), Probability with martingales , Cambridge Mathematical Textbooks, Cambridge University Press
Entire issue dedicated to Martingale probability theory (Laurent Mazliak and Glenn Shafer, Editors). Baldi, Paolo; Mazliak, Laurent; Priouret, Pierre (1991). Martingales and Markov Chains. Chapman and Hall. ISBN 978-1-584-88329-6. Williams, David (1991). Probability with Martingales. Cambridge University Press. ISBN 978-0-521-40605-5.
Schilling, René L. (2005), Measures, Integrals and Martingales, Cambridge: Cambridge University Press, ISBN 978-0-52185-015-5, MR 2200059, Zbl 1084.28001 Williams, David (1991), Probability with Martingales , Cambridge University Press, ISBN 0-521-40605-6 , MR 1155402 , Zbl 0722.60001
Patrick Billingsley: Probability and Measure, John Wiley and Sons, New York, Toronto, London, 1979. Henk Tijms (2004) Understanding Probability ; A lively introduction to probability theory for the beginner, Cambridge Univ. Press. David Williams (1991) Probability with martingales
Probability: A Graduate Course. Springer Texts in Statistics. New York: Springer. doi:10.1007/b138932. ISBN 0-387-22833-0. Williams, David (1991). Probability with Martingales. Cambridge University Press. ISBN 0-521-40605-6. Durrett, Richard (2019). Probability: Theory and Examples (PDF). Cambridge Series in Statistical and Probabilistic ...
In mathematics, uniform integrability is an important concept in real analysis, functional analysis and measure theory, and plays a vital role in the theory of martingales. Measure-theoretic definition
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 expressing it through a set of axioms .