Donald Burkholder’s Work in Martingales and Analysis

  • Burgess Davis
  • Renming Song
Part of the Selected Works in Probability and Statistics book series (SWPS)


The two mathematicians who have most advanced martingale theory in the last seventy years are Joseph Doob and Donald Burkholder. Martingales as a remarkably flexible tool are used throughout probability and its applications to other areas of mathematics. They are central to modern stochastic analysis. And martingales, which can be defined in terms of fair games, lie at the core of mathematical finance. Burkholder’s research has profoundly advanced not only martingale theory but also, via martingale connections, harmonic and functional analysis.


Brownian Motion Harmonic Function Maximal Function Quasiconformal Mapping Singular Integral Operator 
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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematics and Department of StatisticsPurdue UniversityWest LafayetteUSA
  2. 2.Department of MathematicsUniversity of IllinoisUrbanaUSA

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