Bøger i Selected Works in Probability and Statistics serien

His fundamental contributions in this area include results that came to assuage the anxiety of statisticians that were skeptical of nonparametric methodologies, and his work on concepts of dependence has created a large literature.The two volumes are divided into chapters of related works.

This volume contains 30 of David Brillinger's most influential papers. The biologically oriented papers are commented by Tore Schweder from Norway and Haiganoush Preisler from USA, while the point process papers have comments by Peter Guttorp from USA.

This book contains a little more than 20 of Debabrata Basu's most significant articles and writings. Debabrata Basu is internationally known for his highly influential and fundamental contributions to the foundations of statistics, survey sampling, sufficiency, and invariance.

The chapters also span continents and generations, as they present research done over four decades, while crisscrossing the globe.The commentaries provide insight into Terry's contributions to a particular area of research, by summarizing his work and describing its historical and scientific context, motivation, and impact.

This book chronicles Donald Burkholder's thirty-five year study of martingales and its consequences. Here are some of the highlights.Pioneering work by Burkholder and Donald Austin on the discrete time martingale square function led to Burkholder and Richard Gundy's proof of inequalities comparing the quadratic variations and maximal functions of continuous martingales, inequalities which are now indispensable tools for stochastic analysis. Part of their proof showed how novel distributional inequalities between the maximal function and quadratic variation lead to inequalities for certain integrals of functions of these operators. The argument used in their proof applies widely and is now called the Burkholder-Gundy good lambda method. This uncomplicated and yet extremely elegant technique, which does not involve randomness, has become important in many parts of mathematics.The continuous martingale inequalities were then used by Burkholder, Gundy, and Silverstein to prove the converse of an old and celebrated theorem of Hardy and Littlewood. This paper transformed the theory of Hardy spaces of analytic functions in the unit disc and extended and completed classical results of Marcinkiewicz concerning norms of conjugate functions and Hilbert transforms. While some connections between probability and analytic and harmonic functions had previously been known, this single paper persuaded many analysts to learn probability.These papers together with Burkholder's study of martingale transforms led to major advances in Banach spaces. A simple geometric condition given by Burkholder was shown by Burkholder, Terry McConnell, and Jean Bourgain to characterize those Banach spaces for which the analog of the Hilbert transform retains important properties of the classical Hilbert transform.Techniques involved in Burkholder's usually successful pursuit of best constants in martingale inequalities have become central to extensive recent research into two well- known open problems, one involving the two dimensional Hilbert transform and its connection to quasiconformal mappings and the other a conjecture in the calculus of variations concerning rank-one convex and quasiconvex functions.This book includes reprints of many of Burkholder's papers, together with two commentaries on his work and its continuing impact.

As a consequence of Dudley's early work on weak convergence of probability measures on non-separable metric spaces, the Skorohod topology on the space of regulated right-continuous functions can be replaced, in the study of weak convergence of the empirical distribution function, by the supremum norm.

Throughout his career, Schramm made profound and beautiful contributions to mathematics that will have a lasting influence.In these two volumes, Editors Itai Benjamini and Olle Haggstroem have collected some of his papers, supplemented with three survey papers by Steffen Rohde, Haggstroem and Cristophe Garban that further elucidate his work.

During the second half of the 20th century, Murray Rosenblatt was one of the most celebrated and leading figures in probability and statistics. This volume is a celebration of Murray Rosenblatt's stellar research career that spans over six decades, and includes some of his most interesting and influential papers.

His fundamental contributions in this area include results that came to assuage the anxiety of statisticians that were skeptical of nonparametric methodologies, and his work on concepts of dependence has created a large literature.The two volumes are divided into chapters of related works.

The chapters also span continents and generations, as they present research done over four decades, while crisscrossing the globe.The commentaries provide insight into Terry's contributions to a particular area of research, by summarizing his work and describing its historical and scientific context, motivation, and impact.

As a consequence of Dudley's early work on weak convergence of probability measures on non-separable metric spaces, the Skorohod topology on the space of regulated right-continuous functions can be replaced, in the study of weak convergence of the empirical distribution function, by the supremum norm.

This volume contains 30 of David Brillinger's most influential papers. The biologically oriented papers are commented by Tore Schweder from Norway and Haiganoush Preisler from USA, while the point process papers have comments by Peter Guttorp from USA.

During the second half of the 20th century, Murray Rosenblatt was one of the most celebrated and leading figures in probability and statistics. This volume is a celebration of Murray Rosenblatt's stellar research career that spans over six decades, and includes some of his most interesting and influential papers.

This book contains a little more than 20 of Debabrata Basu's most significant articles and writings. Debabrata Basu is internationally known for his highly influential and fundamental contributions to the foundations of statistics, survey sampling, sufficiency, and invariance.

This book chronicles Donald Burkholder's 35-year study of martingales, and its consequences. It reprints most of Burkholder's publications, as well as two commentaries which discuss his work and the remarkable spread of his ideas to many parts of mathematics.

This volume presents selections of Peter J. Peter's amazing career encompasses the majority of statistical developments in the last half-century or about about half of the entire history of the systematic development of statistics. This volume shares insights on these exciting statistical developments with future generations of statisticians.

This volume presents selections of Peter J. Peter's amazing career encompasses the majority of statistical developments in the last half-century or about about half of the entire history of the systematic development of statistics. This volume shares insights on these exciting statistical developments with future generations of statisticians.

Throughout his career, Schramm made profound and beautiful contributions to mathematics that will have a lasting influence.In these two volumes, Editors Itai Benjamini and Olle Haggstroem have collected some of his papers, supplemented with three survey papers by Steffen Rohde, Haggstroem and Cristophe Garban that further elucidate his work.

This volume serves as basic reference for fundamental statistical theory, and at the same time reveals some of its history. The papers are grouped into six themes: fundamental statistics, asymptotic theory, second-order approximations, resampling, applications, and probability.

The late Professor C C (Chris) Heyde (1939-2008), distinguished statistician, mathematician and scientist, worked at a time when many of the foundational building blocks of probability and statistics were being put in place by a phalanx of eminent scientists around the world. This book deals with the memory of Chris.