Burgess Davis is Professor of Statistics & Mathematics at Purdue University. Renming Song is Professor in the Department of Mathematics at the University of Illinois at Urbana-Champaign.

From the reviews:“This book is one of Springer’s Selected Works in Probability and Statistics series offering to readers an opportunity of getting assembled and commented works of distinguished scholars in probability and statistics. … The reviewed book contains reprints of 38 mathematical papers out of Burkholder’s 53 listed (mathematical articles) and four comments by him as well as two commentaries on his work by his students … . This book is recommended for scientists in the field of mathematics and statistics.” (Adriana Horníková, Technometrics, Vol. 54 (1), February, 2012)

• On a class of stochastic approximation processes.- Sufficiency in the undominated case.- Iterates of conditional expectation operators.- On the order structure of the set of sufficient subfields.- Semi-Gaussian subspaces.- Successive conditional expectations of an integrable function.- Maximal inequalities as necessary conditions for almost everywhere convergence.- Martingale transforms. Ann. Math. Statist.- Extrapolation and interpolation of quasilinear operators on martingales.- A maximal function characterization of the class Hp.- Distribution function inequalities for the area integral.- Distribution function inequalities for martingales.- Boundary behaviour of harmonic functions in a half-space and Brownian motion.- One-sided maximal functions and Hp. J. Functional Analysis.- Boundary value estimation of the range of an analytic function.- A sharp inequality for martingale transforms.- Weak inequalities for exit times and analytic functions.- A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional.- Martingale transforms and the geometry of Banach spaces.- A nonlinear partial differential equation and the unconditional constant of the Haar system in Lp.- Boundary value problems and sharp inequalities for martingale transforms.- An elementary proof of an inequality of R. E. A. C. Paley.- Martingales and Fourier analysis in Banach spaces.- A sharp and strict Lp-inequality for stochastic integrals.- A proof of Pełczyn´ski’s conjecture for the Haar system.- Differential subordination of harmonic functions and martingales.- Explorations in martingale theory and its applications.- Strong differential subordination and stochastic integration.- The best constant in the Davis inequality for the expectation of the martingale square function.- Joseph L. Doob.

Burgess Davis is Professor of Statistics & Mathematics at Purdue University. Renming Song is Professor in the Department of Mathematics at the University of Illinois at Urbana-Champaign.

From the reviews:“This book is one of Springer’s Selected Works in Probability and Statistics series offering to readers an opportunity of getting assembled and commented works of distinguished scholars in probability and statistics. … The reviewed book contains reprints of 38 mathematical papers out of Burkholder’s 53 listed (mathematical articles) and four comments by him as well as two commentaries on his work by his students … . This book is recommended for scientists in the field of mathematics and statistics.” (Adriana Horníková, Technometrics, Vol. 54 (1), February, 2012)

• On a class of stochastic approximation processes.- Sufficiency in the undominated case.- Iterates of conditional expectation operators.- On the order structure of the set of sufficient subfields.- Semi-Gaussian subspaces.- Successive conditional expectations of an integrable function.- Maximal inequalities as necessary conditions for almost everywhere convergence.- Martingale transforms. Ann. Math. Statist.- Extrapolation and interpolation of quasilinear operators on martingales.- A maximal function characterization of the class Hp.- Distribution function inequalities for the area integral.- Distribution function inequalities for martingales.- Boundary behaviour of harmonic functions in a half-space and Brownian motion.- One-sided maximal functions and Hp. J. Functional Analysis.- Boundary value estimation of the range of an analytic function.- A sharp inequality for martingale transforms.- Weak inequalities for exit times and analytic functions.- A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional.- Martingale transforms and the geometry of Banach spaces.- A nonlinear partial differential equation and the unconditional constant of the Haar system in Lp.- Boundary value problems and sharp inequalities for martingale transforms.- An elementary proof of an inequality of R. E. A. C. Paley.- Martingales and Fourier analysis in Banach spaces.- A sharp and strict Lp-inequality for stochastic integrals.- A proof of Pełczyn´ski’s conjecture for the Haar system.- Differential subordination of harmonic functions and martingales.- Explorations in martingale theory and its applications.- Strong differential subordination and stochastic integration.- The best constant in the Davis inequality for the expectation of the martingale square function.- Joseph L. Doob.

Burgess Davis is Professor of Statistics & Mathematics at Purdue University. Renming Song is Professor in the Department of Mathematics at the University of Illinois at Urbana-Champaign.

From the reviews:“This book is one of Springer’s Selected Works in Probability and Statistics series offering to readers an opportunity of getting assembled and commented works of distinguished scholars in probability and statistics. … The reviewed book contains reprints of 38 mathematical papers out of Burkholder’s 53 listed (mathematical articles) and four comments by him as well as two commentaries on his work by his students … . This book is recommended for scientists in the field of mathematics and statistics.” (Adriana Horníková, Technometrics, Vol. 54 (1), February, 2012)

• On a class of stochastic approximation processes.- Sufficiency in the undominated case.- Iterates of conditional expectation operators.- On the order structure of the set of sufficient subfields.- Semi-Gaussian subspaces.- Successive conditional expectations of an integrable function.- Maximal inequalities as necessary conditions for almost everywhere convergence.- Martingale transforms. Ann. Math. Statist.- Extrapolation and interpolation of quasilinear operators on martingales.- A maximal function characterization of the class Hp.- Distribution function inequalities for the area integral.- Distribution function inequalities for martingales.- Boundary behaviour of harmonic functions in a half-space and Brownian motion.- One-sided maximal functions and Hp. J. Functional Analysis.- Boundary value estimation of the range of an analytic function.- A sharp inequality for martingale transforms.- Weak inequalities for exit times and analytic functions.- A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional.- Martingale transforms and the geometry of Banach spaces.- A nonlinear partial differential equation and the unconditional constant of the Haar system in Lp.- Boundary value problems and sharp inequalities for martingale transforms.- An elementary proof of an inequality of R. E. A. C. Paley.- Martingales and Fourier analysis in Banach spaces.- A sharp and strict Lp-inequality for stochastic integrals.- A proof of Pełczyn´ski’s conjecture for the Haar system.- Differential subordination of harmonic functions and martingales.- Explorations in martingale theory and its applications.- Strong differential subordination and stochastic integration.- The best constant in the Davis inequality for the expectation of the martingale square function.- Joseph L. Doob.