Donald Burkholder’s Work in Martingales and Analysis

  • DAVIS C ONTENTS
  • Published 2010

Abstract

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. The work of Burkholder and Gundy on martingales in the late sixties and early seventies, which followed Burkholder’s seminal 1966 paper Martingale Transforms [29], led to applications in analysis which revolutionized parts of this subject. Burkholder’s outstanding work in the geometry of Banach spaces, described by Gilles Pisier in this volume, arose from his extension of martingale inequalities to settings beyond Hilbert spaces where the square function approach used in [29] fails. His work in the eighties and

Cite this paper

@inproceedings{ONTENTS2010DonaldBW, title={Donald Burkholder’s Work in Martingales and Analysis}, author={DAVIS C ONTENTS}, year={2010} }