Original Paper

Finance and Stochastics

, Volume 6, Issue 1, pp 3-47

Comments on the life and mathematical legacy of Wolfgang Doeblin

  • Bernard BruAffiliated withLaboratoire de Mathématiques appliquées, Université Paris V, 45 rue des Saints-Pères, 75270 Paris Cedex 06, France
  • , Marc YorAffiliated withLaboratoire de Probabilités et Modèles aléatoires, CNRS-UMR 7599, Universités Paris VI et VII, 4 Place Jussieu, Case 188, 75252 Paris Cedex 05, France (e-mail: deaproba@proba.jussieu.fr)

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Abstract.

This article contains the translation into English of the main results found in the Comptes Rendus Volume of December 2000, dedicated to Wolfgang Doeblin's sealed envelope sent to the Académie des Sciences de Paris in February 1940. The genesis of these results – both from human and scientific perspectives – is discussed, as well as their importance in our present understanding of one-dimensional diffusions.

Key words: Kolmogorov's equation, Doeblin's conditions, regular movement, change of variable formula, diffusion, coupling
JEL Classification: C60, G10
Mathematics Subject Classification (1991): 01A60, 01A70, 60G05, 60H15, 60H30