Oeuvres Complètes--Collected Works

ISBN-13: 9783319418803 / Angielski / Twarda / 2020 / 748 str.

Wolfgang Doeblin; Marc Yor; Bernard Bru

Opis

This book contains all publications of Wolfgang Doeblin (1915-1940). These are accompanied by presentations and commentaries by specialists in the various specific areas of his achievements. Additionally, this book reproduces the pli cachete on -l equation de Kolmogoroff- with commentaries. The modern theory of probability developed between the two World Wars thanks to the very remarkable work of Kolmogorov, Khinchin, S.N. Bernstein, Romanovsky, von Mises, Hostinsky, Onicescu, Frechet, Levy and others, among whom one name shines particularly brightly, that of the young Wolfgang Doeblin. The work, of this young mathematician, tragically cut short by the war, remains even now, and indeed will remain into the future, a model and example of originality and of mathematical power. The present book is conceived and in essence brought to fruition by Marc Yor before his death in 2014. It is dedicated to him."

Recenzje

"It attracted interest not only by mathematicians or some probability theory specialists, but also by the public, which normally would not be that interested in mathematics. ... the editors gathered not only all published articles of W. Doeblin, but also some more papers, especially the 'cahier jaune' (yellow notebook). In comments and annotations the contents of the papers are put into today's context by probability theory specialists. The book is excellent, a large and substantial work." (Silke Göbel, zbMATH 1460.01019, 2021)

Spis treści

J.-M. Bismut, Avant-propos.- H. Föllmer, Geleitwort.- B. Bru, Preface.- Part I The Life of Wolfgang Doeblin March 17, 1915 – June 21, 1940: B. Bru, Biographical Summary.- W. Doeblin, Autobiographical Note.- W. Doeblin (with remarks by B. Bru and E. Seneta), Notice sur les travaux.- List of Works of Wolfgang Doeblin.- Conversion Table.- T. Lindvall, W. Doeblin 1915–1940.- B. Bru and M. Yor, La vie de Doeblin et le pli cacheté 11.668.- B. Bru and M. Yor, Comments on the Life and Mathematical Legacy of Wolfgang Doeblin.-B. Bru and E. Seneta, Two  Letters of W. Doeblin to A. N. Kolmogorov.- Part II Markov Chains: E. Seneta, Doeblin on Discrete Markov Chains.- M. Iosifescu, On Doeblin and Fortet’s paper “Sur des chaînes à liaisons complètes”.- M. Iosifescu,  On Doeblin’s paper “Remarques sur la théorie métrique des fractions continues”.- E. Nummelin, Doeblin’s Theory of Markov Chains on a General Measurable State Space.- W. Doeblin, Sur les chaînes discrètes de Markoff [1936b].- W. Doeblin, Errata 1: Sur les chaînes discrètes de Markoff [1936c].- W. Doeblin, Errata 2: Sur les chaînes discrètes de Markoff [1936d].- W. Doeblin, Sur les chaînes de Markoff [1936e].- W. Doeblin and R. Fortet, Sur deux notes de MM. Kryloff et Bogoliouboff [1937e].- W. Doeblin, Éléments d’une théorie générale des chaînes constantes simples de Markoff [1937f].- W. Doeblin, Le cas discontinu des probabilités en chaîne [1937a].- W. Doeblin, Sur le cas continu des probabilités en chaîne [1937b].- W. Doeblin, and Robert Fortet Sur des chaînes à liaisons complètes [1937c].- W. Doeblin, Sur l’équation de Smoluchowsky [1937d].- W. Doeblin, Sur les propriétés asymptotiques de mouvements régis par certains types de chaînes simples [1938g] (reprint of [1937g] and [1937h]).- W. Doeblin, Sur l’équation matricielle A(t+s) = [A(t)A(s)] et ses applications aux probabilités en chaîne [1938a].-W. Doeblin, Sur l’équation matricielle A(t+s) = [A(t)A(s)] et ses applications au calcul des probabilités [1940a].- W. Doeblin, Sur deux problèmes de M. Kolmogoroff concernant les chaînes dénombrables [1938f].- W. Doeblin, Exposé de la théorie des chaînes simples constantes de Markoff à un nombre fini d’états [1938e].- W. Doeblin, Remarques sur la théorie métrique des fractions continues [1940d.- W. Doeblin, Éléments d’une théorie générale des chaînes simples constantes de Markoff [1940e].-  Part III Sums of Independent Random Variables:  D. M. Mason, Notes on Wolfgang Doeblin’s 1940 paper: L’ensemble de puissances d’une loi de probabilité.- W. Doeblin and P. Lévy, Sur les sommes de variables aléatoires indépendantes à dispersions bornées inférieurement [1936a].-  W. Doeblin, Premiers éléments d’une étude systématique de l’ensemble de puissances d’une loi de probabilité [1938b].-  W. Doeblin, Étude de l’ensemble de puissances d’une loi de probabilité [1938c].- W. Doeblin, Sur les sommes d’un grand nombre de vecteurs aléatoires [1938d].- W. Doeblin, Sur un problème de calcul des probabilités [1939b].- W. Doeblin, Sur les sommes d’un grand nombre de variables aléatoires indépendantes [1939c].- W. Doeblin, Sur l’ensemble de puissances d’une loi de probabilité (1940) [1940f].- W. Doeblin (with remarks by B. Bru and E. Seneta), Sur l’ensemble de puissances d’une loi de probabilité [1946].- Part IV Chapman’s Equations. Part IV.1 Documents Published Before the pli cacheté: W. Doeblin (with a remark by B. Bru), Sur certaines mouvements aléatoires discontinus [1939d].- W. Doeblin, Sur l’équation de Kolmogoroff [1938h].- W. Doeblin, Sur certains mouvements aléatoires [1939a].- W. Doeblin, Sur l’équation de Kolmogoroff [1940b].- W. Doeblin, Sur des mouvements mixtes [1940c].- Part IV.2 The pli cacheté: M. Yor, Présentation du pli cacheté.- W. Doeblin (with remarks by Bernard Bru and Marc Yor), Sur l’équation de Kolmogoroff, pli cacheté déposé le 26 février 1940, ouvert le 18 mai 2000 [1940g/2000].- B. Bru, Notes de lecture du pli cacheté.- W. Doeblin (with remarks by Bernard Bru), Exposé(s) sur l’équation de Chapman [1938i/2000].- Part IV.3 Archival Documents Related to the pli cacheté: B. Bru, Introduction to Doeblin’s “Sur la solution de M. Hostinský de l’équation de Chapman”.- W. Doeblin, Sur la solution de M. Hostinský de l’équation de Chapman [1940h/1993].- W.Doeblin (with an introduction by B. Bru and E. Seneta), Le cahier jaune: Recherche sur l’équation de Chapman. Propriétés communes aux mouvements régis par l’équation de Chapman [1940i/2020].- Part V Appendix: B. Bru and E. Seneta, Postface.- Acknowledgements.- Credits.- Bibliography.- Supplementary Reading. 

 

O autorze

Marc Yor (1949–2014) was Professor at the Pierre et Marie Curie University, Paris VI. He was one of the most eminent specialists in probability theory, with a particular interest in stochastic processes related to Brownian motion and their applications to mathematical finance. A member of the French Academy of Sciences, his numerous students include some very eminent mathematicians.

Bernard Bru is a retired Professor at the René Descartes University, Paris V.  He is a specialist in the history of probability and statistics and has edited the work of some of the major figures in this area, including Laplace, Condorcet, and Cournot.

Blurb

This book contains all of Wolfgang Doeblin's publications. In addition, it includes a reproduction of the pli cacheté on l'équation de Kolmogoroff and previously unpublished material that Doeblin wrote in 1940. The articles are accompanied by commentaries written by specialists in Doeblin's various areas of interest.

The modern theory of probability developed between the two World Wars thanks to the very remarkable work of Kolmogorov, Khinchin, S.N. Bernstein, Romanovsky, von Mises, Hostinsky, Onicescu, Fréchet, Lévy and others, among whom one name shines particularly brightly, that of Wolfgang Doeblin (1915–1940). The work of this young mathematician, whose life was tragically cut short by the war, remains even now, and indeed will remain into the future, an exemplar of originality and of mathematical power.

This book was conceived and in essence brought to fruition by Marc Yor before his death in 2014. It is dedicated to him.